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COMPLEX NUMBERS AND QUADRATIC EQUATIONS — MATHS STD 11 Science — Question

Gujarat BoardEnglish MediumSTD 11 ScienceMATHSCOMPLEX NUMBERS AND QUADRATIC EQUATIONS2 Marks
Question
Express $(5-3 i)^3$ in the form $a+i b$.
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Answer

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

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