Question #348734

Convert 1-i / 2 into trigonometric form


1
Expert's answer
2022-06-07T15:30:22-0400
r2=x2+y2=(1)2+(12)2=54r^2=x^2+y^2=(1)^2+(-\dfrac{1}{2})^2=\dfrac{5}{4}

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

z=1i2z=1-\dfrac{i}{2}

Quadrant IV


r=52,θ=2πtan1(12)r=\dfrac{\sqrt{5}}{2}, \theta=2\pi-\tan^{-1}(\dfrac{1}{2})

or


r=52,θ=πtan1(12)r=-\dfrac{\sqrt{5}}{2}, \theta=\pi-\tan^{-1}(\dfrac{1}{2})


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