1. Tardigrade
  2. Question
  3. Mathematics
  4. A relation φ from C to R is defined by x φ y Leftrightarrow |x|=y. Which one is correct?

Question Error Report

Thank you for reporting, we will resolve it shortly

Back to Question

Q. A relation $\phi$ from C to R is defined by $x\, \phi \,y \Leftrightarrow \left|x\right|=y$. Which one is correct?

Complex Numbers and Quadratic Equations

Solution:

We have
$\left|2+3i\right|=\sqrt{2^{2}+3^{2}}=\sqrt{13} \ne13, $
$\left|3\right|=3 \ne-3$
$\left|1+i\right|=\sqrt{1+1^{2}}=\sqrt{2} \ne2$
$\left|i\right|=1$
$\therefore i \, \phi\, 1$