JEE Mains · Maths · STD 11 - 4.1 complex nubers
Let \({\left( { - \,2\, - \,\frac{1}{3}\,i} \right)^3} = \frac{{x \,+ \,iy}}{{27}}(i\, = \,\sqrt { - 1} ),\) where \(x\) and \(y\) are real numbers, then \(y -x\) equals
- A \(91\)
- B \(-85\)
- C \(85\)
- D \(-91\)
Answer & Solution
Correct Answer
(A) \(91\)
Step-by-step Solution
Detailed explanation
\(\left(-2-\frac{i}{3}\right)^{3}=\left(\frac{x+i y}{27}\right)\) \((-1)^{3}\left(2^{3}+\frac{i^{3}}{27}+3(2) \frac{i^{2}}{9}+3(2)^{2} \cdot \frac{i}{3}\right)=\frac{x-i y}{27}\) \(-\left[8-\frac{i}{27}-\frac{2}{3}+4 i\right]=\frac{x+i y}{27}\)…
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