Answer to Question #349054 in Complex Analysis for Mapula Advice

Question #349054

Convert 1−i/2 into trigonometric form


1
Expert's answer
2022-06-10T10:42:32-0400
"r^2=x^2+y^2=(1)^2+(-\\dfrac{1}{2})^2=\\dfrac{5}{4}"

"\\tan \\theta=\\dfrac{-1\/2}{1}=-\\dfrac{1}{2}"

Quadrant IV


"r=\\dfrac{\\sqrt{5}}{2}, \\theta=2\\pi-\\tan^{-1}\\dfrac{1}{2}"

"z=\\dfrac{\\sqrt{5}}{2}(\\cos(2\\pi-\\tan^{-1}\\dfrac{1}{2})+i\\sin(2\\pi-\\tan^{-1}\\dfrac{1}{2}) )"

Or


"r=-\\dfrac{\\sqrt{5}}{2}, \\theta=\\pi-\\tan^{-1}\\dfrac{1}{2}"

"z=-\\dfrac{\\sqrt{5}}{2}(\\cos(\\pi-\\tan^{-1}\\dfrac{1}{2})+i\\sin(\\pi-\\tan^{-1}\\dfrac{1}{2}) )"


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