Question
Find the modulus of $$ z = \frac{ 11 }{ 125 }+\frac{ 14 }{ 125 }i $$
Answer
The modulus of $ z $ is:
$$ |z| = \dfrac{\sqrt{ 317 }}{ 125 } $$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{ 11 }{ 125 } $ and $ b = \frac{ 14 }{ 125 } $ so:
$$ \begin{aligned}|z| &= \sqrt{ \left(\frac{ 11 }{ 125 }\right)^2 + \left(\frac{ 14 }{ 125 }\right)^2 } \\[1 em]|z| &= \sqrt{ \frac{ 121 }{ 15625 } + \frac{ 196 }{ 15625 } } \\[1 em]|z| &= \sqrt{ \frac{ 317 }{ 15625 } } \\[1 em]|z| &= \frac{\sqrt{ 317 }}{ 125 } \\[1 em] \end{aligned} $$This page was created using
Complex number calculator