Answer to Question #346624 in Complex Analysis for Busi

Question #346624

Convert (1−i)/2 into trigonometric form


1
Expert's answer
2022-06-01T17:52:21-0400
"z=\\dfrac{1}{2}-\\dfrac{1}{2}i"


Quadrant IV


"r^2=(\\dfrac{1}{2})^2+(-\\dfrac{1}{2})^2=\\dfrac{1}{2}"

"r=\\dfrac{\\sqrt{2}}{2}, \\theta=\\tan^{-1}(\\dfrac{-(1\/2)}{1\/2})+2\\pi=\\dfrac{7\\pi}{4}"

"(\\dfrac{\\sqrt{2}}{2}, \\dfrac{7\\pi}{4})"

Or


"r=\\dfrac{\\sqrt{2}}{2}, \\theta=\\tan^{-1}(\\dfrac{-(1\/2)}{1\/2})+\\pi=\\dfrac{3\\pi}{4}"

"(-\\dfrac{\\sqrt{2}}{2}, \\dfrac{3\\pi}{4})"



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