Question
Find the modulus of $$ z = \frac{ 13 }{ 500 }+\frac{ 11 }{ 500 }i $$
Answer
The modulus of $ z $ is:
$$ |z| = \dfrac{\sqrt{ 290 }}{ 500 } $$Explanation
To find modulus of a complex number $ z = a + bi $ we use formula:
$$ |z| = \sqrt{a^2 + b^2} $$In this example we have $ a = \frac{ 13 }{ 500 } $ and $ b = \frac{ 11 }{ 500 } $ so:
$$ \begin{aligned}|z| &= \sqrt{ \left(\frac{ 13 }{ 500 }\right)^2 + \left(\frac{ 11 }{ 500 }\right)^2 } \\[1 em]|z| &= \sqrt{ \frac{ 169 }{ 250000 } + \frac{ 121 }{ 250000 } } \\[1 em]|z| &= \sqrt{ \frac{ 29 }{ 25000 } } \\[1 em]|z| &= \frac{\sqrt{ 290 }}{ 500 } \\[1 em] \end{aligned} $$This page was created using
Complex number calculator