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Question: Answered & Verified by Expert
The modulus and principal argument of the complex number
$\frac{1+2 i}{1-(1-i)^{2}}$ are respectively
MathematicsComplex NumberNDANDA 2017 (Phase 1)
Options:
  • A 1,0
  • B 1,1
  • C 2,0
  • D 2,1
Solution:
2307 Upvotes Verified Answer
The correct answer is: 1,0
We know, if $Z=x+$ iy,$|z|=\sqrt{x^{2}+y^{2}}$
Given, $\frac{1+2 i}{1-(1-i)^{2}}=\frac{1+2 i}{1-\left(1-2 i+i^{2}\right)}=\frac{1+2 i}{1+2 i}=1$
Since, it is purelyreal number, modulus $=1$ and principal argument $=0$

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