# Questions on Algebra: Complex Numbers answered by real tutors!

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Question 994772: solve by elimination

2x+3y=8
x-2y=-3

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Question 994726: Write the complex number 45 in standard form.

Question 994714: two numbers have a difference of 24. find the numbers if the result of adding their sum to their product is a minimum
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two numbers have a difference of 24. find the numbers if the result of adding their sum to their product is a minimum
-----------
f(x) = x(24+x) + x+24 = x^2 + 25x + 24
f'(x) = 2x + 25 = 0
--> Minimum at x = -12.5
--> -12.5 & 11.5

Question 994688: gemma's mean speed on her drive home from cincinnati is 49 mph. if the total trip
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She must have run off the road, wasn't able to finish the posting of the problem.

Question 994462: I need to find the value of a and b. Could you please solve this with each step thank you so much. (a/(x+3))-(b/(x+2))=(3x-2)/((x+3)(x+2))
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solve for :

solve for :

Question 994366: Use the formula (a+b)(a-b) = a2-b2 to complete 99x101
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Use the formula (a+b)(a-b) = a2-b2 to complete 99x101
--> 100^2 - 1 = 9999

Question 993706: Find the real numbers x and y that make the equation true.
-4 + yi = x + 3i

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-4 + yi = x + 3i
---------------
x = -4
y = 3

Question 992802: 1. Find the prime factorization of the Following number prime factorization of 132 is
2. Which the fraction is simplest form 15xy÷12yy=
3. -55÷65y

Question 992396: Write the complex number in standard form.
7 + −16

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What complex number?

John

My calculator said it, I believe it, that settles it

Question 992366: How do you solve the problem 3x^2-15x-7=0 using complete the square?
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... group first two terms together

...factor out

.........complete the square of

to do it, recall that
so, we need to add inside parentheses then subtract it outside parentheses
we do not know , but we know and and we can find

=>=> and
now add it to , and do not forget to multiply by ones you subtract because is in front of parentheses

Question 992286: Find all real or imaginary solutions for the following equation:
(1/x) + 1/(x-1) = (3/2)
I have really been struggling with using imaginaries and fractions. Help is greatly appreciated.
Thank you!

Found 4 solutions by MathTherapy, macston, solver91311, satyareddy22:
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Find all real or imaginary solutions for the following equation:
(1/x) + 1/(x-1) = (3/2)
I have really been struggling with using imaginaries and fractions. Help is greatly appreciated.
Thank you!

2(x - 1) + 2x = 3x(x - 1) ------ Multiplying through by LCD: 2x(x - 1)

(3x - 1)(x - 2) = 0 ------ Factoring trinomial to determine solutions
3x - 1 = 0        OR       x - 2 = 0
OR
Both satisfy the original equation so both are solutions.



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.
Multiply through by x.
.
Multiply through by (x-1)
Multiply each side by (2/3).
Subtract (4/3)x from each side.
Multiply by 3.

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Remember how to add fractions with different denominators. You find the common denominator, convert, and add the numerators. If the two denominators have no factors in common, then the lowest common denominator is simply the product of the two denominators.

Now you have a simple proportion. Cross-multiply, collect like terms, and then solve the resulting quadratic. Said quadratic is factorable and therefore has two real roots.

John

My calculator said it, I believe it, that settles it

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(1/x) + 1/(x-1) = (3/2)
{(x-1)+x}/x(x-1)=3/2
(2x-1/x^2-x)=3/2
2(2x-1)=3(x^2-x)
4x-2=3x^2-3x
3x^2-3x-4x+2=0
3x^2-7x+2=0
3x^2-6x-x+2=0
3x(x-2)-1(x-2)=0
(x-2)(3x-1)=0
=>x-2=0,3x-1=0
=>x=2,x=1/3

Question 992076: What is the vertex of the graph of y = -|4x + 8| + 3?
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The x coordinate of the vertex is the value of x that makes the value of the expression inside the absolute value bars be zero. The y coordinate of the vertex is the value of the function when the value inside the absolute value bars is zero, namely the number outside the absolute value bars.

John

My calculator said it, I believe it, that settles it

Question 991612: I was given two solutions "-i, i" and I have to write an equation where the solution would be -i and i
Found 2 solutions by josgarithmetic, ikleyn:
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Simplifiable to

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.
The equation is

+ 1 = .

It has the roots  "i"  and  "-i".

Question 991554: how many gram of raisin worth php 20 per gram must be mixed with 12 grams of peanuts worth php 18 per gram produce a mixture worth php 19.25 per gram?
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Let = grams of raisins needed
------------

20 grams of raisins are needed
------------
check:

OK

Question 991020: find all seventh root of 3+4i
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.
Find all seventh roots of 3+4i.
-----------------------------------

3 + 4i = , where = .

The seventh roots are    .,

where  k = 0, 1, 2, 3, 4, 5, 6.

See the lesson  How to take a root of a complex number  in this site.

Question 990393: (3-2i)(1+i) + |3+4i|.
Turn this into a+bi form

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.
1.  Let me calculate this term first,  (3-2i)(1+i).

You need simply open parentheses,  make multiplications,  collect common terms and use the fact that  i*i = = -1.  So,
= = = 3 + i -2*(-1) = 3 + i + 2 = 5 + i.

Very good.

2.  Now let consider this term,  |3 + 4i|.

It is the modulus of the complex number  3 + 4i.
As you probably know,  the modulus is the square root of the sum of squares of the components:  r = = = = 5.

So,  the modulus  r  is,  in our case,  simply the real number  5.

Very good.

3.  Now,  the sum (3-2i)(1+i) + |3 + 4i| = (5 + i) + 5 = 10 + i.

That is all.

Congratulations!

Complex numbers and arithmetic operations on them
Complex plane
Addition and subtraction of complex numbers in complex plane
Multiplication and division of complex numbers in complex plane
Raising a complex number to an integer power
How to take a root of a complex number
Solution of the quadratic equation with real coefficients on complex domain
How to take a square root of a complex number
Solution of the quadratic equation with complex coefficients on complex domain

It is free of charge.

Question 990373: ( )+( )+( )=30
Fill the ( ) use this (1,3,5,7,9,11,13,15)

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(9-1)+(11)+(11) = 30

(5)+(11-1)+(15) = 30

(1+5) + (9) + (15) = 30

When you add three odd numbers you will get an odd answer. So you have to apply other strategies to get an even answer of 30 using the odd numbers.

Question 990079: Can I please know what's 6-11=z÷-4

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hi dear,
Here is the steps if you wish to find the value of z.
6-11=z/(-4)
________________________
-5=z/(-4)
multiply out to get
z=20

Question 989973: I keep getting 0 as my answer for this problem, but the answer key says 1/2. Any help would be greatly appreciated!!
Problem: Limit as x is approaching 0 of { {sqrt ( 1+x ) -1 } / ( x ) }

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.
Do you know and did you learn that

= + the terms of lower orders of magnitude at   x ---> 0 ?

In any case,  it is so.

Therefore,   = + the terms of lower orders of magnitude at   x ---> 0,     and further

= + the terms of lower orders of magnitude at   x ---> 0.

It implies that lim = at   x ---> 0.

Question 989679: How 1/i becomes i/(-1)?
Found 3 solutions by MathTherapy, jim_thompson5910, josgarithmetic:
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How 1/i becomes i/(-1)?
It is through a process called: RATIONALIZING the denominator.



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Multiply top and bottom by i

Use the idea that

-------------------------------------------------------

So is equivalent to

Question 989674: Simplify i^-17
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Simplify i^-17
= 1/i^17
= 1/i
= i/(-1)
= -i

Question 989586: solve equation in the complex number system x^4=1
Found 2 solutions by Edwin McCravy, Alan3354:
Answer by Edwin McCravy(13211)   (Show Source):
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I don't believe in just listing answers.  I believe in
showing how to get them.

x-1=0; x+1=0;  x-i=0; x+i=0
x=1;   x=-1;   x=i;   x=-i

Edwin

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solve equation in the complex number system x^4=1
-------------
x = 1
x = -1
x = i
x = -i

Question 989585: express answer of square root of -64 in the form a+bi
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So we see that a = 0 and b = 8.

Question 989588: write expression 4i^3-2i^2+1 in standard form a+bi
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 4i^3-2i^2+1 4i^2*i-2i^2+1 Break up i^3 into i^2*i 4(-1)*i-2(-1)+1 Use the fact that i^2 = -1 -4*i+2+1 -4i+3 3-4i

We're now in standard form a+bi where a = 3, b = -4

Question 989581: solve this equation x^2-2x+5=0 in the complex number system.
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solve this equation x^2-2x+5=0 in the complex number system.
===============
 Solved by pluggable solver: SOLVE quadratic equation (work shown, graph etc) Quadratic equation (in our case ) has the following solutons: For these solutions to exist, the discriminant should not be a negative number. First, we need to compute the discriminant : . The discriminant -16 is less than zero. That means that there are no solutions among real numbers. If you are a student of advanced school algebra and are aware about imaginary numbers, read on. In the field of imaginary numbers, the square root of -16 is + or - . The solution is , or Here's your graph:

===========

Question 989426: Use complex numbers to factor 5x^2+35 completely.
Thank You!!

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5 is a factor and lets ignore it.

you have learnt that

equals plus or minus

Question 989207: Divide and express the results in standard form. Type answer in the form a plus bi
6i divided by 4 minus 7i

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Completely unclear. Can you write what your expression is, symbolically in pure text?

Question 989108: 4^c=16
then c=?

Question 988804: If maple granola cost $2.00 more than Apple granola. And there is 6 bags of maple and 5 bags of Apple granola equaling$56.00. What is the expression of the cost of 5 bags of Apple gronola
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p, price of one bag of Apple Granola
p+2, price of one bag of Maple Granola

Six bags Maple and five bags Apple Granolas, 56 dollar cost. COST! Not price.

, the COST of five bags of the Apple Granola.

Question 988542: Solve the following quadratic equation by the quadratic formula. Simplify the solutions and write them in a + bi form. Answers in comma-separated list.
X square + 2x + 5 =0

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.

.
 Solved by pluggable solver: SOLVE quadratic equation with variable Quadratic equation (in our case ) has the following solutons: For these solutions to exist, the discriminant should not be a negative number. First, we need to compute the discriminant : . The discriminant -16 is less than zero. That means that there are no solutions among real numbers. If you are a student of advanced school algebra and are aware about imaginary numbers, read on. In the field of imaginary numbers, the square root of -16 is + or - . The solution is Here's your graph:

|7 + 24i|

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The SIZE of the complex number;

Question 988241: Let x→-3/2
1/2x+3

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Plug in into in the expression below.

(2-3i)(1-i)-(3-i)(3+i)

Question 988254: Find z such that |z| = 2 and Arg z =

Answer by Edwin McCravy(13211)   (Show Source):
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Edwin

Question 988095: x=5/6;y=3/5

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ok, thx for letting us know.

Question 987497: im having trouble put this problem in stander form
-20+√-75
--------
40

Found 2 solutions by josgarithmetic, Alan3354:
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idk what "putting a problem in stander form" means.
Or standard form.
========================
Step 1, know what you want to do.
Step 2, state what you want to do.

Question 987127: When z = (1+i)/(1-i), prove that z+z²+z³+z⁴=0
Answer by Edwin McCravy(13211)   (Show Source):
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z+z²+z³+z⁴ = i+i²+i³+i⁴ = i+(-1)+(i²×i)+(i²×i²) = i-1+(-1×i)+(-1×-1) =

i-1-i+1 = 0

Edwin