A relation
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 $x \phi y \Leftrightarrow|x|=y .$

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