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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*^{iθ}=*r* (cos *θ*+*i* sin *θ*), where *r* ≠ 0, the inverse of *z* is (1/r)*e*^{−iθ}=(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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