Question:medium

Express the given complex number in the form\( a + ib: (-2-\dfrac{1}{3}i)^3\)

Updated On: Jan 27, 2026
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Solution and Explanation

\((-2-\dfrac{1}{3}i)^3\)

\(=-[2^3+(\dfrac{i}{3})^3+3.(2)(\dfrac{i}{3})(2)(2+\dfrac{i}{3})]\)

\(=-[8+\dfrac{i^3}{27}+2i(2+\dfrac{i}{3})]\)

\(=-[8-\dfrac{i}{27}+4i-\dfrac{2}{3}]\)

\(=-[\dfrac{22}{7}+\dfrac{107}{27}i]\)

\(=-\dfrac{22}{3}-\dfrac{107}{27}i\)  (Ans.)

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