Question

Solve: $iz^3 + z^2 - z + i = 0 \Rightarrow |z| = $ ?

• A. $\dfrac{1}{2}$
• B. $2$
• C. $\dfrac{3}{2}$
• D. $1$

Hint:

Try simple complex values like $z = 1$, $z = i$ for modulus problems with polynomial equations.

Answer 1

The Correct Option is D

Let $z = x + iy$. Use modulus and trial with $z = 1$, $z = i$, etc. Try $z = 1$: \[ iz^3 + z^2 - z + i = i(1)^3 + (1)^2 - 1 + i = i + 1 - 1 + i = 2i \neq 0 \] Try $z = i$: \[ iz^3 + z^2 - z + i = i(i^3) + i^2 - i + i = i(-i) + (-1) - i + i = 1 - 1 = 0 \Rightarrow z = i \Rightarrow |z| = 1 \]