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

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Question : 9 of 52
Marks: +1, -0
(13+3i)3\left(\frac{1}{3}+3i\right)^3
Solution:  
(13+3i)3\left(\frac{1}{3}+3i\right)^3 = (13)3+(3i)3+3(13)2(3i)\left(\frac{1}{3}\right)^3+(3i)^3+3\left(\frac{1}{3}\right)^2 (3i) + 313(3i)23\frac{1}{3}(3i)^2
= 127+27i3+i+9i2\frac{1}{27}+27i^3+i+9i^2 = 127\frac{1}{27} + 27 (- i) + i + 9 (- 1)
= 127\frac{1}{27} - 9 + i (1 - 27) = 1−24327\frac{1-243}{27} + i (- 26) = (−24227)\left(\frac{-242}{27}\right) + (- 26) i
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