A relation ϕ from C to R is defined by

Question:

A relation $\phi$ from $C$ to $R$ is defined by $x \phi y \Leftrightarrow|x|=y$. Which one is correct?

(a) $(2+3 i) \phi 13$

(b) $3 \phi(-3)$

(c) $(1+i) \phi 2$

(d) $i \phi 1$

Solution:

(d) $i \phi 1$

$\because|2+3 i|=\sqrt{13} \neq 13$

$|3| \neq-3$

$|1+i|=\sqrt{2} \neq 2$

and $|\mathrm{i}|=1$

So, $(i, 1) \in \phi$