Question

A relation ϕ from C to R is defined by x ϕ y ⇔ | x | = y. Which one is correct?
(a) (2 + 3 i) ϕ 13
(b) 3 ϕ (−3)
(c) (1 + i) ϕ 2
(d) i ϕ 1

Answer 1

(d) i ϕ 1

$$\begin{gathered} \because \left|2+3i\right|=\sqrt{13}\ne 13 \\ \left|3\right|\ne -3 \\ \left|1+i\right|=\sqrt{2}\ne 2 \\ \mathrm{and}\left|\mathrm{i}\right|=1 \\ \mathrm{So},\left(\mathrm{i},1\right)\in \mathrm{\varphi } \end{gathered}$$