Question #346624

Convert (1−i)/2 into trigonometric form


1
Expert's answer
2022-06-01T17:52:21-0400
z=1212iz=\dfrac{1}{2}-\dfrac{1}{2}i


Quadrant IV


r2=(12)2+(12)2=12r^2=(\dfrac{1}{2})^2+(-\dfrac{1}{2})^2=\dfrac{1}{2}

r=22,θ=tan1((1/2)1/2)+2π=7π4r=\dfrac{\sqrt{2}}{2}, \theta=\tan^{-1}(\dfrac{-(1/2)}{1/2})+2\pi=\dfrac{7\pi}{4}

(22,7π4)(\dfrac{\sqrt{2}}{2}, \dfrac{7\pi}{4})

Or


r=22,θ=tan1((1/2)1/2)+π=3π4r=\dfrac{\sqrt{2}}{2}, \theta=\tan^{-1}(\dfrac{-(1/2)}{1/2})+\pi=\dfrac{3\pi}{4}

(22,3π4)(-\dfrac{\sqrt{2}}{2}, \dfrac{3\pi}{4})



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