SOLUTION: Find square root of 21-20i

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Question 1063158: Find square root of 21-20i
Answer by Fombitz(32388) About Me  (Show Source):
You can put this solution on YOUR website!
z=sqrt%2821-20i%29=x%2Byi
So,
x%5E2-y%5E2=21
2xy=-20
and
z%5E2=x%5E2%2By%5E2=sqrt%2821%5E2%2B20%5E2%29=29
So then,
x%5E2-y%5E2%2Bx%5E2%2By%5E2=21%2B29
2x%5E2=50
x%5E2=25
x=0+%2B-+5
and
2%285%29y=-20
y=0+%2B-+2
So the solution is,
z=5-2i or z=-5%2B2i
z=0+%2B-+%285-i%29