Solveeit Logo
Login

Question

Question: Amplitude of \(\left( \frac{1 - i}{1 + i} \right)\)is...

Amplitude of (1−i1+i)\left( \frac{1 - i}{1 + i} \right)is

A

−π2\frac{- \pi}{2}

B

π2\frac{\pi}{2}

C

π4\frac{\pi}{4}

D

π6\frac{\pi}{6}

Answer

−π2\frac{- \pi}{2}

Explanation

Solution

Sol. z=1−i1+i×1−i1−i=−iz = \frac{1 - i}{1 + i} \times \frac{1 - i}{1 - i} = - i

⇒θ=tan⁡−1(−10)=−π2\Rightarrow \theta = \tan^{- 1}\left( \frac{- 1}{0} \right) = - \frac{\pi}{2}

(Sincezzlies on negative imaginary axis)