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  4. If (x+iy)1/3=2+3i, then 3x+2y is equal to

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Q. If $ {{(x+iy)}^{1/3}}=2+3i, $ then $ 3x+2y $ is equal to

KEAMKEAM 2010Complex Numbers and Quadratic Equations

Solution:

Given, $ {{(x+iy)}^{1/3}}=2+3i $
$ \Rightarrow $ $ x+iy={{(2+3i)}^{3}} $
$ \Rightarrow $ $ x+iy=-46+9i $
$ \Rightarrow $ $ x=-46,y=9 $
$ \therefore $ $ 3x+2y=3\times (-46)+2\times 9 $
$=-138+18=-120 $