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Question Number 125096 by mnjuly1970 last updated on 08/Dec/20

$$...nicecalculus...$$ $$suppose::z=x-iy\mathrm{\&}\sqrt[3]{z}=p+iq$$ $$thenfind::A=\frac{\frac{x}{p}+\frac{y}{q}}{p^2+q^2}=??$$ $$note:i=\sqrt{-1}$$

Answered by MJS_new last updated on 08/Dec/20

$$\sqrt[3]{z}=p+q\mathrm{i}\Rightarrow z=p(p^2-3q^2)-q(q^2-3p^2)\Rightarrow$$ $$\Rightarrow x=p(p^2-3q^2)\wedge y=q(q^2-3p^2)$$ $$\Rightarrow A=-2$$

Commented bymnjuly1970 last updated on 08/Dec/20

$$thanksalotsirMJS.grateful..$$

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