Find (15+8i)^(1/2) in the form of a+ib
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√(15+8i) = a+ib, so 15+8i = (a+ib)² = (a²-b²) + i(2ab)
a²-b² = 15 and ab=4, solve by observation, substitution or otherwise and you get a=4 and b=1, hence
√(15+8i) = 4+i
a²-b² = 15 and ab=4, solve by observation, substitution or otherwise and you get a=4 and b=1, hence
√(15+8i) = 4+i
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15 + 8i = √(15^2 + 8^2) * e^(iarctan(8/15)) = √17*e^(0.49i)
√(15 + 8i) = √17 * e^(0.245i) = √17cos(0.245) + i√17*sin(0.245)
= 4 + i
√(15 + 8i) = √17 * e^(0.245i) = √17cos(0.245) + i√17*sin(0.245)
= 4 + i