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De Moivre’s formula, also called de Moivre’s theorem or de Moivre’s identity, is used to determine the nth power of a complex number. It states that if n is any integer and x is a real number, then $${\left(cos\left(x\right)+isin\left(x\right)\right)}^n=cos\left(nx\right)+isin\left(nx\right)$$, where i is the imaginary unit $$\left(i^2=-1\right)$$. The expression $$cos\left(x\right)+isin\left(x\right)$$ is sometimes reduced to $$cis\left(x\right)$$. De Moivre’s formula is a direct method for solving problems involving powers of complex numbers. In an extended form, it can be used to find the nth roots of a complex number.