Concept:z = x + iyModulus of complex numberr = \(\rm \sqrt{{x}^{2} + y^{2}} \)angle ? is known as a argument or amplitudetan ? = \( \rm \frac{y}{x}\)cos2? + sin2? = 1Calculation:Write \(\rm (\sqrt{3} + i)^{30}\) in polar form\(\rm (\sqrt{3} + i) = r(cos? + i sin ?)\)Where, r = \(\rm \sqrt{\sqrt{3}^{2} + 1^{2}} \) = 2and tan ? =\( \rm \frac{1}{\sqrt{3}}\)? = tan-1(\(\rm \frac{1}{\sqrt{3}}\))\(\rm (\sqrt{3} + i)^{30}\) = 230 (cos 30? + i sin 30?)Given\(\rm (\sqrt{3} + i)^{30}\) = 229(a + ib),a = 2 cos 30?, b = 2 sin 30?a2 + b2 = 4 (cos2 30? + sin2 30?) = 4