Question

Graph the complex number and find its modulus.

$5+2i$

Short answer

The modulus of the complex number $5+2i$ is $\left|z\right|=\sqrt{29}$.

Step-by-step solution

Step 1. Given Information.

The given complex number is $5+2i$.

The modulus of the number is found using the formula $\left|z\right|=\sqrt{a^2+b^2}$

Step 2. Applying the operations.

The given complex number is $5+2i$. Comparing with standard form of complex number $z=a+ib$.

Here a$=5$and b$=2$

Using the formula $\left|z\right|=\sqrt{a^2+b^2}$

$\Rightarrow \left|z\right|=\sqrt{5^2+2^2}$

$\Rightarrow \left|z\right|=\sqrt{25+4}$

$\Rightarrow \left|z\right|=\sqrt{29}$