Question

A relation $\varphi$ from C to R is defined by $x\varphi y\iff \left|x\right|=y$, which one is correct?

• A. $(2+3i)\varphi 13$
• B. $3\varphi (-3)$
• C. $(1+i)\varphi 2$
• D. $i\varphi 1$

Answer 1

The correct option is D $i\varphi 1$

$|2+3i|=\sqrt{2^2+3^2}=\sqrt{13}\ne 13$

$\left|3\right|=3\ne -3$

$|1+i|=\sqrt{1+1^2}=\sqrt{2}\ne 2$

$\left|i\right|=1$

$\therefore i\varphi 1$