Question

Express (√3+√2)(2√3-i) in the form a+ib

Answer 1

Answer:

your solution is as follows

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Step-by-step explanation:

$so \: given \: complex \: number \: is \\ z = ( \sqrt{3} + \sqrt{2} \: )(2 \sqrt{3} - i \: ) \\ \\ = \sqrt{3} (2 \sqrt{ 3} - i) + \sqrt{2} ( 2\sqrt{3} - i) \\ \\ = 6 - \sqrt{3} i + 2 \sqrt{6} - \sqrt{2} i \\ \\ = 6 + 2 \sqrt{6} - \sqrt{3} i - \sqrt{2} i \\ \\ a + ib = 6 + 2 \sqrt{6} - ( \sqrt{3} + \sqrt{2} )i \\ \\ equating \: real \: and \: imaginary \: parts \\ we \: get \\ \\ a = 6 + 2 \sqrt{6} \: \: ; \: b = - ( \sqrt{3} + \sqrt{2} \: )$