Find the modulus and the argument of the complex number $$z = -\sqrt{3} + i$$

Asked by Pragya Singh | 1 year ago |  94

##### Solution :-

The complex number is

$$z = -\sqrt{3} + i$$

Let rcosθ = $$-\sqrt{3}$$   and rsinθ = 1

$$(rcosθ)^2 + (rsinθ)^2 =(-\sqrt{3})^2+(-1)^2$$

$$r^2=3+1=4LLL$$ $$[cos^2\theta+sin^2\theta=1]$$

$$r=\sqrt{4}$$ = 2LLL[ Conventionally, r > 0]

Modulus = 2

$$2cosθ=-\sqrt{3}$$ and 2sinθ = 1

$$cosθ =\dfrac{-\sqrt{3}}{2}$$ and sinθ = $$\dfrac{1}{2}$$

$$\theta=\pi-\dfrac{\pi}{6}=\dfrac{5\pi}{6}$$LL[As θ lies in the II quadrant]

Thus, the modulus and argument of the complex number $$-\sqrt{3} + i$$ are 2 and $$\dfrac{5\pi}{6}$$

Answered by Abhisek | 1 year ago

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