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NDA 2023 Maths · Mathematics · Complex Numbers and Quadratic Equations · medium

The modulus of the complex number ((1+i)^3/(1-i) is

Single correct option

The modulus of the complex number (1+i)31−i\dfrac{(1+i)^3}{1-i} is
  1. A. 222\sqrt2
  2. B. 22
  3. C. 2\sqrt2
  4. D. 44
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Answer: (B) 22

Use ∣z1/z2∣=∣z1∣/∣z2∣|z_1/z_2|=|z_1|/|z_2| and ∣zn∣=∣z∣n|z^n|=|z|^n. Since ∣1+i∣=∣1−i∣=2|1+i|=|1-i|=\sqrt2, the modulus is (2)32=(2)2=2\dfrac{(\sqrt2)^3}{\sqrt2}=(\sqrt2)^2=2. The option 222\sqrt2 is only the numerator's modulus, and 2\sqrt2 is the result of forgetting the cube.
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Original question written in the NDA 2023 Maths pattern and checked twice for the correct answer. Not an official question paper. How we write and check questions · Corrections policy · Report a mistake