Question

Graph the complex number and find its modulus.

$7-3i$

Short answer

The modulus of the complex number $7-3i$ is $\left|z\right|=\sqrt{58}$.

Step-by-step solution

Step 1. Given Information.

The given complex number is $7-3i$.

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$7-3i$. Comparing with standard form of complex number $z=a+ib$.

Here a$=7$ and b$=-3i$

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

$\Rightarrow \left|z\right|=\sqrt{7^2+{(-3)}^2}$

$\Rightarrow \left|z\right|=\sqrt{49+9}$

$\Rightarrow \left|z\right|=\sqrt{58}$