If $z=3+5 i$, then $z^3+\bar{z}+198$ is equal to

Question

Aicharya · Accepted Answer

We have, $ \begin{aligned} z & =3+5 i \ 	herefore \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, $ \begin{aligned} z^3+\bar{z}+198 & =-198+10 \dot{i}+3-5 i+198 \ & =3+5 i \end{aligned} $

If $z=3+5 i$, then $z^3+\bar{z}+198$ is equal to

Solution