SOLUTION: If (x+yi)^2=8-6i, find the values of x and y. I approached this by thinking that x=a and y=b. So I just plugged in the numbers to x and y. => (8-6i)(8-6i) => 64-48i-48i+24i^

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Question 863289: If (x+yi)^2=8-6i, find the values of x and y.
I approached this by thinking that x=a and y=b. So I just plugged in the numbers to x and y.
=> (8-6i)(8-6i)
=> 64-48i-48i+24i^2
=> 64-96i+24i^2
=> 64-96i+24-1
=> 64-96i+23
=> 87-96i
But when I looked up the answer in the book it said x=3 and y=-1.
I'm really hoping you can help tell me how to properly solve this problem.
Thanks and have a good day.

Answer by ewatrrr(24785)   (Show Source): You can put this solution on YOUR website!

Hi
(x+yi)^2=8-6i
x^2 + 2xyi - y^2 = 8 -6i
the Idea is (and You will see this again..Apples to Apples
2xyi = -6i
y = -3/x
x^2 - 9/x^2 = 8
x^4 - 8x^2 -9 = 0
(x^2 -9)(x^2 + 1)= 0 Using real roots only
x^2 = 9
x = ± 3
y = -3/x
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