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Question: The amplitude of \(|z| = 1,(z \neq - 1)\) is....

The amplitude of ∣z∣=1,(z≠−1)|z| = 1,(z \neq - 1) is.

A

z=x+iy,z = x + iy,

B

(z−1z+1)\left( \frac{z - 1}{z + 1} \right)

C

∣2z−1∣+∣3z−2∣|2z - 1| + |3z - 2|

D

1/21/2

Answer

z=x+iy,z = x + iy,

Explanation

Solution

Let −amp(−z)=tan⁡−1yx−(tan⁡−1yx−π)=π- amp( - z) = \tan^{- 1}\frac{y}{x} - \left( \tan^{- 1}\frac{y}{x} - \pi \right) = \pi

(z)=tan⁡−1sin⁡α1−cos⁡α(z) = \tan^{- 1}\frac{\sin\alpha}{1 - \cos\alpha}