Question

express in a+ib form and state values of a and b i(9+6i)(2-i)^-1

Answer 1

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$= > i(9 + 6i) {(2 - i)}^{ - 1} \\ \\ = > (9i + 6 {i}^{2} )( \frac{1}{2 - i} ) \\ \\ = > (9i + 6 {i}^{2} )( \frac{1}{2 - i} \times \frac{2 +i }{2 + i} ) \\ \\ = > (9 i + 6 {i}^{2}) \times ( \frac{2 + i}{5} ) \\ \\ = > ( 9i-6)( \frac{2 + i}{5} ) \\ \\ = > (9i-6)( \frac{2 + i}{5} ) \\ \\ = > \frac{18i-12+9{i}^{2}-6i}{5} = > -\frac{21}{5} + \frac{12}{5} i \\ \\ \: by \: comparing \: we \: get : \\ \\ a =- \frac{21}{5} \\ \\ and \\ \\ b = -\frac{12}{5}$
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