SOLUTION: find the square root of (1-2 sq rt 2i)?

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Question 667803: find the square root of (1-2 sq rt 2i)?
Found 2 solutions by Alan3354, MathLover1:
Answer by Alan3354(69443) About Me  (Show Source):
You can put this solution on YOUR website!
find the square root of (1-2 sq rt 2i)?
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z+=+1+-+sqrt%288%29i
Mag+=+sqrt%281+%2B+8%29+=+3
Angle = atan(sqrt(8)) =~ 70.5288
z = 3cis(70.5288)
sqrt(z) = sqrt(3)cis(35.2644)
sqrt(z) = sqrt(3)*sqrt(2/3) + i*sqrt(3)*sqrt(1/3)
= sqrt(2) + i

Answer by MathLover1(20849) About Me  (Show Source):
You can put this solution on YOUR website!
sqrt+%281-2%2A+sqrt%28+2i%29%29

sqrt%281-2%2A+sqrt%28+2i%29%29...........since sqrt%28+i%29=%28-1%29%5E%281%2F4%29=root%284%2C-1%29, we have

sqrt+%281-2%2Aroot%284%2C-1%29+sqrt%28+2%29%29

sqrt+%281-2%2Aroot%284%2C-1%29+sqrt%28+2%29%29..........since root%284%2C-1%29=%281%2Bi%29%2Fsqrt%282%29, we have

sqrt+%281-2%2A%28%281%2Bi%29%2Fsqrt%282%29%29+sqrt%28+2%29%29

sqrt+%281-2%2A%28%281%2Bi%29%2Fcross%28sqrt%282%29%29%29+cross%28sqrt%28+2%29%29%29

sqrt+%281-2%2A%281%2Bi%29%29

sqrt+%281-2%2B2i%29

sqrt+%28-1%2B2i%29

0.786151377757-1.2720196495%2Ai