inverse of a complex number

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If z is a non-zero complex number and z=x+yi, the (multiplicative) inverse of z, denoted by z−1 or 1/z, is When z is written in polar form, so that z=re=r (cos θ+i sin θ), where r ≠ 0, the inverse of z is (1/r)e=(1/r)(cos θ−i sin θ). If z is represented by P in the complex plane, then z−1 is represented by Q, where ∠xOQ=−∠xOP and |OP| . |OQ| =1.

Subjects: Mathematics.

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