Convert the given complex number in polar form -1 + i and evaluate

Asked by Abhisek | 1 year ago |  70

##### Solution :-

The complex number is -1+i

Let rcosθ = -1 and rsinθ = 1

$$r^2cos^2θ + r^2sin^2θ = (-1)^2+1^2$$

$$r^2(cos^2θ + sin^2θ) =1+1$$

$$r^2=2$$

$$r=\sqrt{2}$$

$$\sqrt{2} cosθ = -1 \;and\; \sqrt{2}sinθ = 1$$

$$cosθ =- \dfrac{1}{\sqrt{2}}and \sqrt{2}sinθ =1$$

$$θ ...(\pi-\dfrac{\pi}{4})...-\dfrac{3\pi}{4}L$$ [As θ lies in the II quadrant]

It can be written,

-1+i = rcosθ + irsinθ

=$$\sqrt{2}cos \dfrac{3\pi}{4}+i\sqrt{2}sin \dfrac{3\pi}{4}$$

$$\sqrt{2}(cos \dfrac{3\pi}{4}+isin \dfrac{3\pi}{4})$$

Answered by Pragya Singh | 1 year ago

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