Question

Graph the complex number and find its modulus.

$\sqrt{3}+i$

Short answer

The modulus of the complex number$\sqrt{3}+i$ is $\left|z\right|=2$.

Step-by-step solution

Step 1. Given Information.

The given complex number is $\sqrt{3}+i$.

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 $\sqrt{3}+i$. Comparing with standard form of complex number $z=a+ib$.

Here a$=\sqrt{3}$ and b$=1$

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

$\Rightarrow \left|z\right|=\sqrt{{\sqrt{3}}^2+1^2}$

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

$\Rightarrow \left|z\right|=2$