Tutors Answer Your Questions about Complex Numbers (FREE)
Question 994772: solve by elimination
2x+3y=8
x2y=3
Answer by MathLover1(11324) (Show Source):
You can put this solution on YOUR website!
Solved by pluggable solver: Solving a System of Linear Equations by Elimination/Addition 
Lets start with the given system of linear equations
In order to solve for one variable, we must eliminate the other variable. So if we wanted to solve for y, we would have to eliminate x (or vice versa).
So lets eliminate x. In order to do that, we need to have both x coefficients that are equal but have opposite signs (for instance 2 and 2 are equal but have opposite signs). This way they will add to zero.
So to make the x coefficients equal but opposite, we need to multiply both x coefficients by some number to get them to an equal number. So if we wanted to get 2 and 1 to some equal number, we could try to get them to the LCM.
Since the LCM of 2 and 1 is 2, we need to multiply both sides of the top equation by 1 and multiply both sides of the bottom equation by 2 like this:
Multiply the top equation (both sides) by 1
Multiply the bottom equation (both sides) by 2
So after multiplying we get this:
Notice how 2 and 2 add to zero (ie )
Now add the equations together. In order to add 2 equations, group like terms and combine them
Notice the x coefficients add to zero and cancel out. This means we've eliminated x altogether.
So after adding and canceling out the x terms we're left with:
Divide both sides by to solve for y
Reduce
Now plug this answer into the top equation to solve for x
Plug in
Multiply
Subtract from both sides
Combine the terms on the right side
Multiply both sides by . This will cancel out on the left side.
Multiply the terms on the right side
So our answer is
,
which also looks like
(, )
Notice if we graph the equations (if you need help with graphing, check out this solver)
we get
graph of (red) (green) (hint: you may have to solve for y to graph these) and the intersection of the lines (blue circle).
and we can see that the two equations intersect at (,). This verifies our answer. 
Question 994726: Write the complex number 45 in standard form.
Answer by josmiceli(13716) (Show Source):
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
Answer by Alan3354(47455) (Show Source):
You can put this solution on YOUR website! 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
Answer by Alan3354(47455) (Show Source):
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))=(3x2)/((x+3)(x+2))
Answer by MathLover1(11324) (Show Source):
Question 994366: Use the formula (a+b)(ab) = a2b2 to complete 99x101
Answer by Alan3354(47455) (Show Source):
Question 993706: Find the real numbers x and y that make the equation true.
4 + yi = x + 3i
Answer by Alan3354(47455) (Show Source):
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
Answer by Fombitz(25151) (Show Source):
Question 992396: Write the complex number in standard form.
7 + −16
Answer by solver91311(20879) (Show Source):
Question 992366: How do you solve the problem 3x^215x7=0 using complete the square?
Answer by MathLover1(11324) (Show Source):
Question 992286: Find all real or imaginary solutions for the following equation:
(1/x) + 1/(x1) = (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: Answer by MathTherapy(4047) (Show Source): Answer by macston(4006) (Show Source): Answer by solver91311(20879) (Show Source): Answer by satyareddy22(65) (Show Source):
You can put this solution on YOUR website! (1/x) + 1/(x1) = (3/2)
{(x1)+x}/x(x1)=3/2
(2x1/x^2x)=3/2
2(2x1)=3(x^2x)
4x2=3x^23x
3x^23x4x+2=0
3x^27x+2=0
3x^26xx+2=0
3x(x2)1(x2)=0
(x2)(3x1)=0
=>x2=0,3x1=0
=>x=2,x=1/3
Question 992076: What is the vertex of the graph of y = 4x + 8 + 3?
Answer by solver91311(20879) (Show Source):
You can put this solution on YOUR website!
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: Answer by josgarithmetic(13975) (Show Source): Answer by ikleyn(988) (Show Source):
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?
Answer by josmiceli(13716) (Show Source):
Question 991020: find all seventh root of 3+4i
Answer by ikleyn(988) (Show Source):
Question 990393: (32i)(1+i) + 3+4i.
Turn this into a+bi form
Answer by ikleyn(988) (Show Source):
You can put this solution on YOUR website! .
1. Let me calculate this term first, (32i)(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 (32i)(1+i) + 3 + 4i = (5 + i) + 5 = 10 + i.
That is all.
Congratulations!
To learn more on complex numbers, you can read my lessons in this site
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)
Answer by farohw(153) (Show Source):
You can put this solution on YOUR website!
(91)+(11)+(11) = 30
(5)+(111)+(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 611=z÷4
Answer by Timnewman(249) (Show Source):
You can put this solution on YOUR website! hi dear,
Here is the steps if you wish to find the value of z.
611=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 ) }
Answer by ikleyn(988) (Show Source):
Question 989679: How 1/i becomes i/(1)?
Found 3 solutions by MathTherapy, jim_thompson5910, josgarithmetic: Answer by MathTherapy(4047) (Show Source): Answer by jim_thompson5910(33401) (Show Source): Answer by josgarithmetic(13975) (Show Source):
Question 989674: Simplify i^17
Answer by Alan3354(47455) (Show Source):
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): Answer by Alan3354(47455) (Show Source):
Question 989585: express answer of square root of 64 in the form a+bi
Answer by jim_thompson5910(33401) (Show Source):
Question 989588: write expression 4i^32i^2+1 in standard form a+bi
Answer by jim_thompson5910(33401) (Show Source):
You can put this solution on YOUR website!
4i^32i^2+1   4i^2*i2i^2+1  Break up i^3 into i^2*i  4(1)*i2(1)+1  Use the fact that i^2 = 1  4*i+2+1   4i+3   34i  
We're now in standard form a+bi where a = 3, b = 4
Question 989581: solve this equation x^22x+5=0 in the complex number system.
Answer by Alan3354(47455) (Show Source):
Question 989426: Use complex numbers to factor 5x^2+35 completely.
Thank You!!
Answer by thesvw(67) (Show Source):
Question 989207: Divide and express the results in standard form. Type answer in the form a plus bi
6i divided by 4 minus 7i
Answer by josgarithmetic(13975) (Show Source):
Question 989108: 4^c=16
then c=?
Answer by Alan3354(47455) (Show Source):
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
Answer by josgarithmetic(13975) (Show Source):
You can put this solution on YOUR website! 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 actual answer to the question asked is:
, 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 commaseparated list.
X square + 2x + 5 =0
Answer by macston(4006) (Show Source):
Question 988540: Write without absolute value symbols.(Simplify your answer completely.)
7 + 24i
Answer by josgarithmetic(13975) (Show Source):
Question 988241: Let x→3/2
1/2x+3
Answer by EdenWolf(454) (Show Source):
Question 988278: Please provide all the steps, on how to get the answer please.
(23i)(1i)(3i)(3+i)
Answer by Fombitz(25151) (Show Source):
Question 988254: Find z such that z = 2 and Arg z =
Please answer this
Answer by Edwin McCravy(13211) (Show Source):
Question 988095: x=5/6;y=3/5
Answer by Alan3354(47455) (Show Source):
Question 987497: im having trouble put this problem in stander form
20+√75

40
Found 2 solutions by josgarithmetic, Alan3354: Answer by josgarithmetic(13975) (Show Source): Answer by Alan3354(47455) (Show Source):
You can put this solution on YOUR website! 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)/(1i), prove that z+z²+z³+z⁴=0
Answer by Edwin McCravy(13211) (Show Source):

Older solutions: 1..45, 46..90, 91..135, 136..180, 181..225, 226..270, 271..315, 316..360, 361..405, 406..450, 451..495, 496..540, 541..585, 586..630, 631..675, 676..720, 721..765, 766..810, 811..855, 856..900, 901..945, 946..990, 991..1035, 1036..1080, 1081..1125, 1126..1170, 1171..1215, 1216..1260, 1261..1305, 1306..1350, 1351..1395, 1396..1440, 1441..1485, 1486..1530, 1531..1575, 1576..1620, 1621..1665, 1666..1710, 1711..1755, 1756..1800, 1801..1845, 1846..1890, 1891..1935, 1936..1980, 1981..2025, 2026..2070, 2071..2115, 2116..2160, 2161..2205, 2206..2250, 2251..2295, 2296..2340, 2341..2385, 2386..2430, 2431..2475, 2476..2520, 2521..2565, 2566..2610, 2611..2655, 2656..2700, 2701..2745, 2746..2790, 2791..2835, 2836..2880, 2881..2925, 2926..2970, 2971..3015, 3016..3060, 3061..3105, 3106..3150, 3151..3195, 3196..3240, 3241..3285, 3286..3330, 3331..3375, 3376..3420, 3421..3465, 3466..3510, 3511..3555, 3556..3600, 3601..3645, 3646..3690, 3691..3735, 3736..3780, 3781..3825, 3826..3870, 3871..3915, 3916..3960, 3961..4005, 4006..4050, 4051..4095, 4096..4140, 4141..4185, 4186..4230, 4231..4275, 4276..4320, 4321..4365, 4366..4410, 4411..4455, 4456..4500, 4501..4545, 4546..4590, 4591..4635, 4636..4680, 4681..4725, 4726..4770, 4771..4815, 4816..4860, 4861..4905, 4906..4950, 4951..4995, 4996..5040, 5041..5085, 5086..5130, 5131..5175, 5176..5220, 5221..5265, 5266..5310, 5311..5355, 5356..5400, 5401..5445
