If z = 3+5i, then z 3 + ¯ z + 198 = Options: A . &nbsp -3-5i B . &nbsp -3+5i C . &nbsp 3+5i D . &nbsp 3-5i

If z = 3+5i, then z3 + ¯z + 198 =

Question -

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

Options:

A . -3-5i

B . -3+5i

C . 3+5i

D . 3-5i

Answer: Option C
:
C

z = 3+5i , $¯ z$ = 3-5i

⇒ $z^{3} = (3 + 5 i)^{3} = 3^{3} + (5 i)^{3} + 3.3.5 i (3 + 5 i)$

= -198+10i

Hence, $z^{3} + ¯ z$ + 198 = 10i-198+3-5i+198 = 3+5i .

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