poveli1e

2022-01-30

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

Gordon Stephens

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

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