Question

If (x+ iy) 1/3 = 2+3i, then 3x+2y is equal to (a) -20 (b) -60 (c) -120 (d) 60​

Answer 1

$\textbf{Given:}$

$(x+i\,y)^{\frac{1}{3}}=2+3\,i$

$\textbf{To find:}$

$\text{The value of 3x+2y }$

$\textbf{Solution:}$

$\text{Consider,}$

$(x+i\,y)^{\frac{1}{3}}=2+3\,i$

$\text{Cubing on bothsides, we get}$

$x+i\,y=(2+3\,i)^3$

$x+i\,y=2^3+(3i)^3+3(4)(3i)+3(2)(-9)$

$x+i\,y=8-27\,i+36\,i-54$

$x+i\,y=-46+9\,i$

$\text{Separating real and imaginary parts, we get}$

$x=-46\;\;\text{and}\;\;y=9$

$\text{Now,}$

$3x+2y$

$=3(-46)+2(9)$

$=-138+18$

$=-120$

$\textbf{Answer:}$

$\textbf{The value of \bf\,3x+2y is -120}$

$\textbf{Option (C) is correct}$

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Answer 2

Answer:

answer is -120(c)..........