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Solve-for-complex-numbers-x-2-3-y-2-5-x-y-2-8-10x-y-7-14i-




Question Number 173072 by Shrinava last updated on 06/Jul/22
Solve for complex numbers:   { ((((∣x∣^2 )/3)  +  ((∣y∣^2 )/5)  =  ((∣x + y∣^2 )/8))),((10x  +  y  =  7  +  14i)) :}
$$\mathrm{Solve}\:\mathrm{for}\:\mathrm{complex}\:\mathrm{numbers}: \\ $$$$\begin{cases}{\frac{\mid\mathrm{x}\mid^{\mathrm{2}} }{\mathrm{3}}\:\:+\:\:\frac{\mid\mathrm{y}\mid^{\mathrm{2}} }{\mathrm{5}}\:\:=\:\:\frac{\mid\mathrm{x}\:+\:\mathrm{y}\mid^{\mathrm{2}} }{\mathrm{8}}}\\{\mathrm{10x}\:\:+\:\:\mathrm{y}\:\:=\:\:\mathrm{7}\:\:+\:\:\mathrm{14}\boldsymbol{\mathrm{i}}}\end{cases} \\ $$

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