AP EAMCET · Maths · Complex Number
Define \(f: C \rightarrow \mathrm{R}\) by \(f(z)=|z|, \forall z \in C\). Then, which of the following is false ?
- A \(f(-z)=f(z), \forall z \in C\)
- B \(f(\bar{z})=f(z), \forall z \in C\)
- C \(f\left(z^2\right)=(f(z))^2, \forall z \in C\)
- D \(f\left(z_1^2+z_2^2\right)=f\left(z_1^2\right)+f\left(z_2^2\right), \forall z_1, z_2 \in C\)
Answer & Solution
Correct Answer
(D) \(f\left(z_1^2+z_2^2\right)=f\left(z_1^2\right)+f\left(z_2^2\right), \forall z_1, z_2 \in C\)
Step-by-step Solution
Detailed explanation
Given, \(f(z)=|z|\) (a) \(f(-z)=f(z)\) is true \[ |z|=|-z| \] (b) \[ f(\bar{z})=f(z) \text { is true } \] \[ |\bar{z}|=|z| \] (c)…
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