Question:
A relation $\phi$ from $\mathrm{C}$ to $\mathrm{R}$ 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) $i \phi 1$
We have $|i|=\sqrt{1^{2}+0^{2}}=1$
Thus, $i \phi 1$ satisfies $x \phi y \Leftrightarrow|x|=y .$