The Cartesian form of complex number $z=4\left(\cos 300^{\circ}\right)$, where $i=\sqrt{1}$ is

The Cartesian form of complex number $z=4\left(\cos 300^{\circ}\right)$, where $i=\sqrt{1}$ is
  1. $2-2 \sqrt{3} i$
  2. $1+\sqrt{3} i$
  3. $1-\sqrt{3} i$
  4. $2+2 \sqrt{3} i$

Solution

$4\left(\cos 300^{\circ}+i \sin 300^{\circ}\right)=4\left(\frac{1}{2}-\frac{\sqrt{3}}{2} i\right)=2-2 \sqrt{3} i$

Asked in: MHT CET 2022 (08 Aug Shift 1)

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