A relation R from C to R is defined by xRy iff |x| = y. Which of the following is correct?

(2 + 3i) R 13 3 R (–3) (1 + i) R 2 iR1

iR1

$|2+3 i|=\sqrt{(2)^2+(3)^2}=\sqrt{13} \neq 13$ ∴ (2 + 3i) R 13 is wrong. $|3|=\sqrt{(3)^2+0^2}=\sqrt{9}=3 \neq-3$ ∴ 3R (–3) is wrong $|1+i|=\sqrt{(1)^2+(1)^2}=\sqrt{2} \neq 2$ ∴  (1 + i) R2 is wrong $|1+i|=\sqrt{(1)^2+(1)^2}=\sqrt{2} \neq 2$ ∴  iR1 is correct. Hence (4) is the correct answer.