[u][b]Complex Inverses[/b][/u][b]: [/b][math]\frac{1}{z},\text{ with }z\ne0[/math][b][b][br][br]Example: [/b][/b]Express [math]\frac{1}{3+4i}[/math] [b] in the standard form of [math]a+bi[/math][/b][b].[br]Solution: [math]\frac{1}{3+4i}=\frac{1}{3+4i}\cdot\frac{3-4i}{3-4i}=\frac{3−4i}{9+16}=\frac{3}{25}−\frac{4}{25}i[/math][/b][b].[/b][br][b][br]Fact:[/b] If [math]z=a+bi\ne0[/math], then [math]a^2+b^2\ne0[/math] and [math]\frac{1}{z}=\frac{1}{a+bi}=\frac{a}{a^2+b^2}−\frac{b}{a^2+b^2}i[/math][br][br][b][u]Geometry for[/u] [/b][math]\frac{1}{z},z\ne0[/math]. [br]Geometric understanding comes best by using the polar or exponential representation.[br]That is, if [math]z=|z|cis(θ)=|z|e^{iθ}[/math] then [math]\frac{1}{z}=\frac{1}{\left|z\right|}cis(−θ)=\frac{1}{\left|z\right|}e^{−iθ}[/math].[center][br][img 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[/img][/center]