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

Rajasthan 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= a3 - 3a2b+ 3b2a - b3]
= 125 - 225i - 135 + 27i = -10 - 198i

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