SOLUTION: find the square root of (-15+8i)

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Question 838942: find the square root of (-15+8i)
Answer by Fombitz(32388) About Me  (Show Source):
You can put this solution on YOUR website!
%28a%2Bbi%29%28a%2Bbi%29=a%5E2%2Babi%2Babi%2B%28bi%29%5E2
%28a%2Bbi%29%28a%2Bbi%29=%28a%5E2-b%5E2%29%2B2abi
1.a%5E2-b%5E2=-15
2.2ab=8
From eq. 2,
ab=4
a=4%2Fb
a%5E2=16%2Fb%5E2
Substitute into eq. 1,
16%2Fb%5E2-b%5E2=-15
16-b%5E4=-15b%5E2
b%5E4-15b%5E2-16=0
%28b%5E2-16%29%28b%5E2%2B1%29=0
Only the real solution.
b%5E2-16=0
b%5E2=16
b=4
From eq. 2,
ab=4
a%284%29=4
a=1
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sqrt%28%28-15%2B8i%29%29=1%2B4i