AP EAMCET · Maths · Complex Number
If \(z_1=1-2 i ; z_2=1+i\) and \(z_3=3+4 i\), then \(\left(\frac{1}{z_1}+\frac{3}{z_2}\right) \frac{z_3}{z_2}=\)
- A \(13-6 i\)
- B \(13-3 i\)
- C \(6-\frac{13}{2} i\)
- D \(\frac{13}{2}-3 i\)
Answer & Solution
Correct Answer
(D) \(\frac{13}{2}-3 i\)
Step-by-step Solution
Detailed explanation
We have, \[ \begin{aligned} & z_1=1-2 i, z_2=1+i, \\ & z_3=3+4 i \end{aligned} \] Now, \(\left(\frac{1}{z_1}+\frac{3}{z_2}\right) \frac{z_3}{z_2}=\left(\frac{1}{1-2 i}+\frac{3}{1+i}\right)\left(\frac{3+4 i}{1+i}\right)\)…
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