find square roots of -8-6i
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Rashmi Bajpayee 8 years, 7 months ago
Let (x + iy)2 = -8 - 6i => x2 - y2 + 2xyi = -8 -6i => x2 - y2 = -8 ..........(i)
and 2xy = -6 => 4x2y2 = 36
Since (x2 + y2)2 = (x2 - y2)2 + 4x2y2 => (x2 + y2)2 = (-8)2 + 36 => (x2 + y2)2 = 100
=> x2 + y2 = 10 .........(ii)
On solving eq. (i) and eq. (ii), we get x = +-1 and y = +-3
Therefore, x - iy = +-(1 - 3i)
(-8-6i)1/2 = +-(1 - 3i)
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