Write the complex number $\frac{\sqrt{3}+i}{\sqrt{3}-i}$ in standard form?

Answer & Explanation

Gordon Stephens

Beginner2022-01-31Added 10 answers

Step 1
By rationalising the denominator, we get the standard form.
$\frac{\sqrt{3}+i}{\sqrt{3}-i}$
Multiply and divide by $(\sqrt{3}+i)$ $\Rightarrow \frac{{(\sqrt{3}+i)}^{2}}{(\sqrt{3}-i)\times (\sqrt{3}+i)}$ $\Rightarrow \frac{{(\sqrt{3}+i)}^{2}}{3+1}$ $\Rightarrow {\left(\frac{\sqrt{3}+i}{2}\right)}^{2}$