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

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Question : 7 of 52
Marks: +1, -0
[(13+i73)+(4+i13)]−(−43+i)\left[\left(\frac{1}{3} + i \frac{7}{3}\right) + \left(4 + i \frac{1}{3}\right)\right] - \left(-\frac{4}{3} + i\right)
Solution:  
[(13+i73)+(4+i13)]−(−43+i)\left[\left(\frac{1}{3} + i \frac{7}{3}\right) + \left(4 + i \frac{1}{3}\right)\right] - \left(-\frac{4}{3} + i\right)
= [(13+4)+i(73+13)]\left[\left(\frac{1}{3} + 4\right) + i\left(\frac{7}{3} + \frac{1}{3}\right)\right] - (−43+i)\left(-\frac{4}{3} + i\right) = 1+123+i7+13\frac{1+12}{3} + i \frac{7+1}{3} + 43\frac{4}{3} - i
= 133+i83+43−i\frac{13}{3} + i \frac{8}{3} + \frac{4}{3} - i = 133+43+i(83−1)\frac{13}{3} + \frac{4}{3} + i\left(\frac{8}{3} - 1\right) = 13+43+i(8−33)\frac{13+4}{3} + i\left(\frac{8-3}{3}\right)
= 173+53i\frac{17}{3} + \frac{5}{3} i
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