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Inverse of Complex Number
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MasterWuMathematics
The Multiplicative Inverse of a Complex Number
The multiplicative inverse of a complex number exists such that z∙z^-1 = 1. To find the inverse, let z = a+ib and z^-1 = c+id. Now, when we multiply z and z^-1, we get: z∙z^-1 = (a+ib)(c+id)=ac+iad+ibc+i^2bd=(ac-bd)+i(ad+bc) Knowing the result that z∙z^-1 = 1, we can equate the components: ac-bd = 1 ad+bc = 0 Solving these simultaneously ...
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