Question

complex number please do answer​

Answer 1

Answer:

hey here is your solution

pls mark it as brainliest

Step-by-step explanation:

$so \: here \\ \\ \frac{ - \sqrt{7} - i \sqrt{3} }{ \sqrt{7} - i \sqrt{3} } + \frac{28 + i \sqrt{2} }{ \sqrt{7} - i \sqrt{ 3} } \\ \\ = \frac{ - \sqrt{7} - i \sqrt{3} \: +2 \sqrt{7} + i \sqrt{2} }{ \sqrt{7} - i \sqrt{3} } \\ \\ = \frac{i \sqrt{2} - i \sqrt{3} + \sqrt{7} }{ \sqrt{7} - i \sqrt{3} } \\ \\ so \: \: conjugate \: of \: \sqrt{7} - i \sqrt{3} \: \: is \\ \sqrt{7} + i \sqrt{3} \\ \\ thus \: then \\ rationalising \: denominator \\ \\ \frac{i \sqrt{2} - i \sqrt{3} + \sqrt{7} }{ \sqrt{7} - i \sqrt{3} } \: \times \: \frac{ \sqrt{7} + i \sqrt{3} }{ \sqrt{7} + i \sqrt{3} } \\ \\ = \frac{(i \sqrt{2} - i \sqrt{3} + \sqrt{7} )( \sqrt{7} + i \sqrt{3} \: )}{( \sqrt{7} ) {}^{2} - (i \sqrt{3}) {}^{2} } \\ \\ \\ = \frac{ \sqrt{14}i - \sqrt{21} \: i + 7 + \sqrt{6} i {}^{2} - 3i {}^{2} + \sqrt{21}i }{7 - 3i {}^{2} } \\ \\ \\ = \frac{ \sqrt{14i} + 7 - 3( - 1) + \sqrt{6} ( - 1)}{7 - 3( - 1)} \\ \\ = \frac{ \sqrt{14}i + (7 + 3) - \sqrt{6} }{7 + 3} \\ \\ = \frac{ \sqrt{14} i + 10 - \sqrt{6} }{10} \\ \\ a + ib \: = \frac{ \sqrt{14}i }{10} \: - \: \frac{10 - \sqrt{6} }{10} \\ \\ equating \: real \: and \: imaginary \: parts \\ we \: get \: then \\ \\ a = - ( \frac{10 - \sqrt{6} }{10} \: ) \\ \\ b = \frac{ \sqrt{14} }{10}$