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4-1.Complex numbers
medium
જો $z = 3 + 5i,\,\,$ તો $\,{z^3} + \bar z + 198 = $
A
$ - 3 - 5i$
B
$ - 3 + 5i$
C
$3 + 5i$
D
$3 - 5i$
Solution
(c) $z = 3 + 5i$, $\bar z = 3 – 5i$
$ \Rightarrow \,$${z^3} = {(3 + 5i)^3} = {3^3} + {(5i)^3} + 3.3.5i\,(3 + 5i)$
$ = – 198 + 10i$
Hence, ${z^3} + \bar z + 198 = 10\,i – 198 + 3 – 5\,i + 198 = 3 + 5\,i$.
Standard 11
Mathematics
