Question

A relation ϕ from C to R is defined by x ϕ y ⇔ $\left|x\right|$ = y. Which one is correct?

(a) (2 + 3i) ϕ 13
(b) 3ϕ (−3)
(c) (1 + i) ϕ 2
(d) i ϕ 1

Answer 1

(d) i ϕ 1

We have $\left|i\right|=\sqrt{1^2+0^2}=1$
Thus, i ϕ 1 satisfies x ϕ y ⇔ $\left|x\right|$ = y.