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

$\varphi :c\to R;x\varphi y\iff |x|=y$
y is always positive (B is false)
$i\varphi 1\Rightarrow |i|=1$
$\therefore (i,1)$ do satisfy the relation.
$x\varphi y;|(2+3i)|=\sqrt{13}$ (A is false)
$|(1+i)|=\sqrt{2}$ (c is false)