The modulus and amplitude of 1+2 i 1-(1-i)^2 are - Vidyadip

MCQ

The modulus and amplitude of $\frac{1+2 i}{1-(1-i)^2}$ are

A
$\sqrt{2}$ and $\frac{\pi}{6}$
✓
1 and $0$
C
1 and $\frac{\pi}{3}$
D
1 and $\frac{\pi}{4}$

✓

Answer

Correct option: B.

1 and $0$

(B)
$\frac{1+2 i}{1-(1-i)^2}=\frac{1+2 i}{1-(1-1-2 i)}=\frac{1+2 i}{1+2 i}=1+0 i$
Modulus =1
Amplitude $\theta=\tan ^{-1}\left(\frac{0}{1}\right)=0$

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