Find the modulus and the argument of the comp | vedclass

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Question

(A) Given complex number is $z = -\sqrt{3} + i$.Let $r \cos 	heta = -\sqrt{3}$ and $r \sin 	heta = 1$.On squaring and adding,we get:$r^{2}(\cos^{2}

Vedclass · Accepted Answer

Modulus $= 2$,Argument $= \frac{5\pi}{6}$

Vedclass · Answer

(A) Given complex number is $z = -\sqrt{3} + i$.Let $r \cos 	heta = -\sqrt{3}$ and $r \sin 	heta = 1$.On squaring and adding,we get:$r^{2}(\cos^{2} 	heta + \sin^{2} 	heta) = (-\sqrt{3})^{2} + (1)^{2}$$r^{2} = 3 + 1 = 4$$r = 2$ (since $r > 0$).Thus,the modulus is $2$.Now,$2 \cos 	heta = -\sqrt{3} \Rightarrow \cos 	heta = -\frac{\sqrt{3}}{2}$ and $2 \sin 	heta = 1 \Rightarrow \sin 	heta = \frac{1}{2}$.Since $\cos 	heta  0$,the angle $	heta$ lies in the $II$ quadrant.The reference angle is $\alpha = \frac{\pi}{6}$.Therefore,$	heta = \pi - \frac{\pi}{6} = \frac{5\pi}{6}$.The modulus is $2$ and the argument is $\frac{5\pi}{6}$.

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

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