Question

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

• A. $(2+3i)R13$
• B. $3R(-3)$
• C. $(1+i)R2$
• D. $iR1$.

Answer 1

The correct option is D $iR1$.

$|2+3i|=\sqrt{(2{)}^2+(3{)}^2}=\sqrt{13}\ne 13$
$\therefore (2+3i)R13$ is wrong.
$|3|=\sqrt{(3{)}^2+0^2}=\sqrt{9}=3\ne -3$
$\therefore 3R(-3)$ is wrong
$|1+i|=\sqrt{(1{)}^2+(1{)}^2}=\sqrt{2}\ne 2$
$\therefore (1+i)R^2$ is wrong
$|i|=\sqrt{0^2+(1{)}^2}=\sqrt{1}=1$
$\therefore iR1$ is correct.
$\therefore$ The correct answer is $D$.