A) \[4({{a}^{2}}+{{b}^{2}})\]
B) \[4({{a}^{2}}-{{b}^{2}})\]
C) \[4({{b}^{2}}-{{a}^{2}})\]
D) None of these
Correct Answer: B
Solution :
\[{{(x+iy)}^{1/3}}=a+ib\]Þ\[(x+iy)={{(a+ib)}^{3}}\] \[={{a}^{3}}+3{{a}^{2}}.ib+3a.{{(ib)}^{2}}+{{(ib)}^{3}}\] \[={{a}^{3}}-3a{{b}^{2}}+i(3{{a}^{2}}b-{{b}^{3}})\] Equating real and imaginary parts, we get \[\frac{x}{a}={{a}^{2}}-3{{b}^{2}}\]and \[\frac{y}{b}=3{{a}^{2}}-{{b}^{2}}\] \[\therefore \] \[\frac{x}{a}+\frac{y}{b}=4({{a}^{2}}-{{b}^{2}})\]
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