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^

Algebra.Com
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  

RELATED QUESTIONS


(x+yi)(2-3i)=-13i.
I want to find the values of x and... (answered by robertb)

Find the real numbers x and y that make the equation true.
-3 + yi = x +... (answered by josmiceli)

Find The Value Of X and Y... (answered by solve_for_x)

I am having trouble with this problem, and I can't seem to figure where to start:

Find  (answered by richard1234,Boreal,ikleyn)

Find the values of x and y:... (answered by ankor@dixie-net.com)

What are the values of x and y when (5−3i)−(x+... (answered by lynnlo)

What are the values of x and y when (5−3i)−(x+... (answered by josmiceli)

Find The Value Of X And Y boy sollving complex numbers equation... (answered by Fombitz)

find real numbers of x and y such that: (x+yi)(2+i) = 2x-... (answered by DrBeeee)