The polar form of ${\left(i^{41}\right)}^3$ is

Important Questions on Complex Numbers

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Gamma Question Bank for Engineering Mathematics>Chapter 5 - Complex Numbers>Assignment>Q 33

If $z=\frac{-4+2\sqrt{3}i}{5+\sqrt{3}i}$, then the value of $\arg \left(z\right)$ is

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Gamma Question Bank for Engineering Mathematics>Chapter 5 - Complex Numbers>Assignment>Q 34

If $z=\cos \frac{\pi }{4}+i\sin \frac{\pi }{6}$, then

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Gamma Question Bank for Engineering Mathematics>Chapter 5 - Complex Numbers>Assignment>Q 35

The sum of principal arguments of complex numbers $1+i,-1+i\sqrt{3},-\sqrt{3}-i,\sqrt{3}-i,i,-3i,2,-1$ is

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Gamma Question Bank for Engineering Mathematics>Chapter 5 - Complex Numbers>Assignment>Q 36

If $z_1,z_2$ and $z_3,z_4$ are two pairs of conjugate complex numbers, then $\arg \left(\frac{z_1}{z_3}\right)+\arg \left(\frac{z_2}{z_4}\right)$ is

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Gamma Question Bank for Engineering Mathematics>Chapter 5 - Complex Numbers>Assignment>Q 37

If $\arg z=\frac{\pi }{4}$, then

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Gamma Question Bank for Engineering Mathematics>Chapter 5 - Complex Numbers>Assignment>Q 38

The argument of $-2+2\sqrt{3}i$ is

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Gamma Question Bank for Engineering Mathematics>Chapter 5 - Complex Numbers>Assignment>Q 39

The polar form of complex number $\sqrt{3}+i$ is

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Gamma Question Bank for Engineering Mathematics>Chapter 5 - Complex Numbers>Assignment>Q 40

The amplitude of $\frac{1}{i}$ is equal to