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Complex Numbers and Quadratic Equations — Maths STD 11 Science — Question

CBSE BoardEnglish MediumSTD 11 ScienceMathsComplex Numbers and Quadratic Equations2 Marks
Question
Express $(5 - 3i)^3$ in the form $a + ib.$
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Answer

We have, $(5-3i)^3= 5^3 - 3 \times 5^2 \times (3i) + 3 \times 5 (3i)^2 - (3i)^3$
$ [(a-b)^3= a^3 - 3a^2b+ 3b^2a - b^3]$
$= 125 - 225i - 135 + 27i = -10 - 198i$

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