quality:corruption
Example

For x = 30 ∘ {\displaystyle x=30^{\circ }} and n = 2 {\displaystyle n=2}, de Moivre's formula asserts that (cos (30 ∘) + i sin (30 ∘)) 2 = cos (2 ⋅ 30 ∘) + i sin (2 ⋅ 30 ∘), {\displaystyle \left(\cos(30^{\circ })+i\sin(30^{\circ })\right)^{2}=\cos(2\cdot 30^{\circ })+i\sin(2\cdot 30^{\circ }),} or equivalently that (3 2 + i 2) 2 = 1 2 + i 3 2. {\displaystyle \left({\frac {\sqrt {3}}{2}}+{\frac {i}{2}}\right)^{2}={\frac {1}{2}}+{\frac {i{\sqrt {3}}}{2}}.} In this example, it is easy to check the validity of the equation by multiplying out the left side.