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

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(D) Given $z = 3+5i$,then the conjugate is $\bar{z} = 3-5i$.First,calculate $z^3$:$z^2 = (3+5i)^2 = 9 + 25i^2 + 30i = 9 - 25 + 30i = -16 + 30i$.$z^3 =

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$3+5i$

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(D) Given $z = 3+5i$,then the conjugate is $\bar{z} = 3-5i$.First,calculate $z^3$:$z^2 = (3+5i)^2 = 9 + 25i^2 + 30i = 9 - 25 + 30i = -16 + 30i$.$z^3 = z^2 \cdot z = (-16 + 30i)(3 + 5i) = -48 - 80i + 90i + 150i^2$.Since $i^2 = -1$,$z^3 = -48 + 10i - 150 = -198 + 10i$.Now,substitute these into the expression:$z^3 + \bar{z} + 198 = (-198 + 10i) + (3 - 5i) + 198$.$= (-198 + 198) + (10i - 5i) + 3 = 0 + 5i + 3 = 3 + 5i$.

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

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