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NCERT Class XI Mathematics - Complex Numbers and Quadratic Equations - Solutions

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Question : 10 of 52
Marks: +1, -0
(−2−13i)3\left(-2-\frac{1}{3}i\right)^3
Solution:  
(−2−13i)3\left(-2-\frac{1}{3}i\right)^3 = (−2)3+(−13i)3(-2)^3+\left(-\frac{1}{3}i\right)^3 + 3(−2)2(−13i)+3(−2)(−13i)23(-2)^2\left(-\frac{1}{3}i\right)+3(-2)\left(-\frac{1}{3}i\right)^2
= - 8 - 127i3\frac{1}{27} i^3 - 4i - 23i2\frac{2}{3} i^2 = - 8 - 127\frac{1}{27} (- i) - 4i - 23\frac{2}{3} (- 1)
= - 8 + 127i\frac{1}{27} i - 4i + 23\frac{2}{3} = (−8+23)+(127−4)i\left(-8+\frac{2}{3}\right)+\left(\frac{1}{27}-4\right)i
= (−24+23)+(1−10827)i\left(\frac{-24+2}{3}\right)+\left(\frac{1-108}{27}\right)i = −223\frac{-22}{3} + −10727\frac{-107}{27} i
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