Question
Find the modulus of $$ z = \frac{ 283 }{ 2000 }+\frac{ 3911 }{ 50000 }i $$
Answer
The modulus of $ z $ is:
$$ |z| = \dfrac{\sqrt{ 65351546 }}{ 50000 } $$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{ 283 }{ 2000 } $ and $ b = \frac{ 3911 }{ 50000 } $ so:
$$ \begin{aligned}|z| &= \sqrt{ \left(\frac{ 283 }{ 2000 }\right)^2 + \left(\frac{ 3911 }{ 50000 }\right)^2 } \\[1 em]|z| &= \sqrt{ \frac{ 80089 }{ 4000000 } + \frac{ 15295921 }{ 2500000000 } } \\[1 em]|z| &= \sqrt{ \frac{ 32675773 }{ 1250000000 } } \\[1 em]|z| &= \frac{\sqrt{ 65351546 }}{ 50000 } \\[1 em] \end{aligned} $$This page was created using
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