Question 761600: What is the square root of -7+8i
Answer by stanbon(75887)   (Show Source):
You can put this solution on YOUR website! What is the square root of -7+8i
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Use polar notation:
r = sqrt[7^2 + 8^2] = 10.83
theta = arctan(-8/7) = 131.2 degrees
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-7+8i = 10.83cis(131.2)
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sqrt(-7+8i) = sqrt(10.83)cis[(131.2+360n)/2]
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If n = 0 you get sqrt(10.83)cis(65.6 degrees)
If n = 1 you get sqrt(10.83)cis(245.50 degrees)
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Convert to rectangular notation:
sqrt = 3.29[cos(65.5)+isin(65.5)] = 1.36 + 3i
sqrt = 3.29[cos(245.5)+isin(245.5)] = -1.36 -3i
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Cheers,
Stan H.
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