Questions on Algebra: Complex Numbers answered by real tutors!

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Algebra: Complex Numbers

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Question 1784: so I can get a answer using complex numbers I am taking Intermediae Algerbra in college and my final is in the moring. I got as far as the answer you gave me but the answer my teacher gave me 2+i and 2-i. I am confused as how she got that answer by using the qudratic equation using (Imagery Solution). Thank you so much I have been struggling over this problem all weekend.
Click here to see answer by longjonsilver(2297)

Question 1790: who descover imagnary numbers

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Question 2171: Hi,
when you have something, say
3(2 + i) is that equal to 3(2 + 0i) or 3( 2 + 1i)?
Thanks in advance.
Click here to see answer by longjonsilver(2297)

Question 2295: what is:
i squared
i cubed
and i to the fourth power?
Click here to see answer by longjonsilver(2297)

Question 3084: X+Y
O (3-2i)+(3+2i)=6
Does O mean to put (3-2i)put into (3+2i)?
Click here to see answer by thechamp1011(19)

Question 3196: how do you find the complex solutions to X^2+2=2x
Click here to see answer by mixerimaythyme(7)

Question 3352: 22 is 80% of what?/ 32 is whatt percent of 56?/ and if x is 8 when y is 18, and x and y vary directly, what is the value of y when x is 10?
Click here to see answer by longjonsilver(2297)

Question 3340: how would you go about solving "i" to the 91st power getting either a positive or negative "i"
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Question 3449: z is an element of C such that [(z)/(z-i)] is real.How can I show that z is imaginary.
Click here to see answer by khwang(438)

Question 4005: I know that i^2 is -1 but what is i^3 and i^4 ?
Click here to see answer by longjonsilver(2297)

Question 4027: find all real and/or complex solutions:
(x+1)^(-3/2)=8
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Question 4138: Z=1+i√3. Find the smallest positive integer n for which z^n is real and evaluate z^n for this value of n. Show that there is no integral value of n for which z^n is imaginary.
Click here to see answer by khwang(438)

Question 4358: transform the following expression to the standard form.
(2-radical 6i)squared
Click here to see answer by khwang(438)

Question 4028: (x+1)^(-3/2)=8
Solve the complex solution
Click here to see answer by khwang(438)

Question 4355: transform the product of (2-i)(-7-3i) to the standard form.
Click here to see answer by rapaljer(3620)

Question 4443: Find the quotient, write the answer in standard form.
(8-4i)/(5-2i)
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Question 4618: How does one write the complex conjugate for -2+3i?
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Question 4619: What is the abosolute value of 12 - 5i?
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Question 4620: How does one plot 2 - 5i?
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Question 4621: What is (2 - 3i) / (1 - 4i)
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Question 4622: What is (4 - 3i)^2
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Question 4638: How do you write an equation with one root 2 + 3i?
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Question 4638: How do you write an equation with one root 2 + 3i?
Click here to see answer by rapaljer(3620)

Question 4632: i^91=?
This question was asked previously (question 3340), and the given soluttion was to find where i^91 came in the cycle of i. However I learned another way to do it, and I was wondering if it is correct.
Take the given question i^91:
i^91 = i^90 + 1
= i^90 * i^1
= (i^2)^45*i^1
= -1^45 * i^1
= -1 * i
= -i

Click here to see answer by longjonsilver(2297)

Question 4649: This quadratic equation has no real solution...so does that mean imaginary numbers are involved? How do you solve it?
4x^2 - 3x + 8 = 0
Click here to see answer by rapaljer(3620)

Question 4656: What is the exact value of -81^(3/2)

Click here to see answer by Earlsdon(4898)

Question 4644: What is (2 - 3i)(1 - 4i)?

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Question 4673: Solve for x: 625^x = 125.
Click here to see answer by xcentaur(357)

Question 4674: Solve for x: 6^x = 492.
Click here to see answer by Earlsdon(4898)

Question 4643: What is (2 + 2i)(2 - 2i)?

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Question 4672: How does one find the exact value of (-64)^(2/3)?
Click here to see answer by xcentaur(357)

Question 4672: How does one find the exact value of (-64)^(2/3)?
Click here to see answer by rapaljer(3620)

Question 4647: What is the square root of -72?
Click here to see answer by longjonsilver(2297)

Question 4670: What is the exact value of (-16)^(5/4)?

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Question 4671: What is the difference between (-16)^(5/4) and -16^(5/4)?

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Question 4753: How do you multiply to find the number in standard form of an exponent?

Click here to see answer by longjonsilver(2297)

Question 4786: Hello...
I am having some trouble with a proof. I am to use:
(a + bi)(a - bi)
The problem asks:
Show that for a + bi not equal to 0 this product is a positive real number.
Thanks for your help.

Click here to see answer by ichudov(404)

Question 5318: what is sqrt of i?
Click here to see answer by longjonsilver(2297)

Question 5318: what is sqrt of i?
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Question 3614: what is i^4n+1?
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Question 5325: How to you solve 1 divided by 2-i?
I have tried to multiply by numerator and denominator by 2-i. It doesn't seem right
Click here to see answer by ichudov(404)

Question 5902: 4square root -49 - 3square root -25
Click here to see answer by Abbey(339)

Question 5963: Working with complex numbers and I need to find all the real numbers
x and y that satisfy the equation 3x + 1 + 2yi = x – 5i
Thank you.
Click here to see answer by AnlytcPhil(958)

Question 6274: I have to find all real and imaginary numbers. My guess is to factor, but I don't think it does.
3x(x)+ 2x + 1 = 0
Click here to see answer by xcentaur(357)

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