TS EAMCET · Maths · Complex Number
If \((2 x-y+1)+i(x-2 y-1)=2-3 i\), then the multiplicative inverse of \((x-i y)\) is
- A \(\frac{15}{41}+\frac{12}{41} i\)
- B \(\frac{6}{29}+\frac{15}{29} i\)
- C \(\frac{15}{29}+\frac{6}{29} i\)
- D \(\frac{12}{41}+\frac{15}{41} i\)
Answer & Solution
Correct Answer
(D) \(\frac{12}{41}+\frac{15}{41} i\)
Step-by-step Solution
Detailed explanation
\(2x-y+1=2 \implies 2x-y=1\) \(x-2y-1=-3 \implies x-2y=-2\) \(2(2x-y) - (x-2y) = 2(1) - (-2)\) \(4x-2y-x+2y = 2+2\) \(3x = 4 \implies x = \frac{4}{3}\) \(y = 2x-1 = 2\left(\frac{4}{3}\right)-1 = \frac{8}{3}-1 = \frac{5}{3}\) \(x-iy = \frac{4}{3} - i\frac{5}{3} = \frac{4-5i}{3}\)…
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