If z is any complex number and iz^{3}+z^{2}-z+i=0, where i=\sqrt{-1}, then what is the value of (|z|+1)^{2}?
- A. 1
- B. 4 ✓
- C. 81
- D. 121
Correct Answer: B. 4
Explanation
Factor the given equation: z^2(iz+1) + i(iz+1) = 0 \Rightarrow (z^2+i)(iz+1) = 0. Thus, z^2 = -i or iz = -1 \Rightarrow z = i. In both cases, taking the modulus gives |z| = 1. Therefore, (|z|+1)^2 = (1+1)^2 = 4.
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