SOLUTION: Express 3+4i in polar form and hence determine the exact square roots of 3+4i in the form a + ib, where a, b are real numbers.

Question 867405: Express 3+4i in polar form and hence determine the exact square roots of 3+4i in
the form a + ib, where a, b are real numbers.
Answer by stanbon(75887) (Show Source): You can put this solution on YOUR website!
Express 3+4i in polar form and hence determine the exact square roots of 3+4i in
the form a + ib, where a, b are real numbers.
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r = sqrt[3^2+4^2] = sqrt[25] = 5
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angle = arctan(4/3) = 36.87 degrees
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So, 3+4i = 5[cis(36+87+360n)]
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sqrt(3+4i) = ?
Let n = 0, then sqrt(3+4i) = sqrt(5)[cis(36.87/2)]
Let n = 1, then sqrt(3+4i) = sqrt(5)[cis[(36.87+360)/2]
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Cheers,
Stan H.
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