TS EAMCET · Maths · Complex Number
If \(z=3+5 i\), then \(z^3+\bar{z}+198\) is equal to
- A \(-3-5 i\)
- B \(-3+5 i\)
- C \(3-5 i\)
- D \(3+5 i\)
Answer & Solution
Correct Answer
(D) \(3+5 i\)
Step-by-step Solution
Detailed explanation
We have, \[ \begin{aligned} z & =3+5 i \\ \therefore \quad \bar{z} & =3-5 i \\ z^3 & =z^2 \cdot z=(3+5 i)^2(3+5 i) \\ & =(9-25+30 i)(3+5 i) \\ & =(-16+30 i)(3+5 i) \\ & =-48-150+10 i \\ & =-198+10 i \end{aligned} \] Now,…
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