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NDA 2024
Exam
NDA
Year
2024
Subject
Mathematics
Chapter
Complex Number

NDA 2024 · Mathematics · Complex Number

If z is any complex number and i z^3+z^2-z+i=0 , where i= -1 , then...

If zz is any complex number and iz3+z2−z+i=0i z^3+z^2-z+i=0, where i=−1i=\sqrt{-1}, then what is the value of (∣z∣+1)2?(|z|+1)^2 ?

Options

  1. A1
  2. B4
  3. C81
  4. D121

Correct answer

B. 4

Step-by-step solution

∵iz3+z2−z+i=0 put z=i∴i4+i2−i+i=0⇒1−1−i+i=0\begin{aligned} & \because i z^3+z^2-z+i=0 \\ & \text{ put } \qquad z=i \\ & \therefore i^4+i^2-i+i=0 \\ & \Rightarrow 1-1-i+i=0 \end{aligned} Hence, [∣z∣+1]2=[∣i∣+1]2=22=4[|z|+1]^2=[|i|+1]^2=2^2=4
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