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
r2=x2+y2=(1)2+(12)2=54r^2=x^2+y^2=(1)^2+(-\dfrac{1}{2})^2=\dfrac{5}{4}

tanθ=1/21=12\tan \theta=\dfrac{-1/2}{1}=-\dfrac{1}{2}

Quadrant IV


r=52,θ=2πtan112r=\dfrac{\sqrt{5}}{2}, \theta=2\pi-\tan^{-1}\dfrac{1}{2}

z=52(cos(2πtan112)+isin(2πtan112))z=\dfrac{\sqrt{5}}{2}(\cos(2\pi-\tan^{-1}\dfrac{1}{2})+i\sin(2\pi-\tan^{-1}\dfrac{1}{2}) )

Or


r=52,θ=πtan112r=-\dfrac{\sqrt{5}}{2}, \theta=\pi-\tan^{-1}\dfrac{1}{2}

z=52(cos(πtan112)+isin(πtan112))z=-\dfrac{\sqrt{5}}{2}(\cos(\pi-\tan^{-1}\dfrac{1}{2})+i\sin(\pi-\tan^{-1}\dfrac{1}{2}) )


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