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# Express $\;(5-3i)^{3}\;$ in the form of $\;a+ib$

$(a)\;-10-198i\qquad(b)\;-5 - 128i \qquad(c)\;-2-198i \qquad(d)\;-128i$

Answer : $\;-10-198i$
Explanation :
We have , $\;(5-3i)^{3}\; = 5^{3}-3 \times 5^{2} \times (3i) + 3 \times 5 \times (3i)^{2} - (3i)^{3}$
$= 125 +225i -135 + 27i$
$= -10-198i\;.$