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

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Question

(C) Given $z = 3 + 5i$,the conjugate is $\bar{z} = 3 - 5i$. First,calculate $z^3$: $z^3 = (3 + 5i)^3 = 3^3 + (5i)^3 + 3(3)(5i)(3 + 5i)$ $z^3 = 27 + 12

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$3 + 5i$

Vedclass · Answer

(C) Given $z = 3 + 5i$,the conjugate is $\bar{z} = 3 - 5i$. First,calculate $z^3$: $z^3 = (3 + 5i)^3 = 3^3 + (5i)^3 + 3(3)(5i)(3 + 5i)$ $z^3 = 27 + 125i^3 + 45i(3 + 5i)$ $z^3 = 27 - 125i + 135i + 225i^2$ Since $i^2 = -1$,$z^3 = 27 + 10i - 225 = -198 + 10i$. Now,substitute into the expression: $z^3 + \bar{z} + 198 = (-198 + 10i) + (3 - 5i) + 198$ $= (-198 + 198) + (10i - 5i) + 3$ $= 3 + 5i$.

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

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