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Question: The argument of the complex number \(1/3\) is....

The argument of the complex number 1/31/3 is.

A

∣z∣=1|z| = 1

B

ω=z−1z+1\omega = \frac{z - 1}{z + 1}

C

z≠−1)z \neq - 1)

D

Re(ω){Re}(\omega)

Answer

z≠−1)z \neq - 1)

Explanation

Solution

=tan⁡−1(cot⁡α2)=tan⁡−1{tan⁡(π2−α2)}=π2−α2= \tan^{- 1}\left( \cot\frac{\alpha}{2} \right) = \tan^{- 1}\left\{ \tan\left( \frac{\pi}{2} - \frac{\alpha}{2} \right) \right\} = \frac{\pi}{2} - \frac{\alpha}{2}

because it lies in second quadrant.