Question

Express in the form of a + ib ​

Answer 1

Given -

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$\bf\longrightarrow{\bigg[ \bigg( \dfrac{1}{3} + i\dfrac{7}{3} \bigg) + \bigg( 4 + i\dfrac{1}{3} \bigg) \bigg] - \bigg( - \dfrac{4}{3} + i \bigg)}$

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Solution -

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$\rm\implies{\bigg[ \bigg( \dfrac{1}{3} + i\dfrac{7}{3} \bigg) + \bigg( 4 + i\dfrac{1}{3} \bigg) \bigg] - \bigg( - \dfrac{4}{3} + i \bigg)}$

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$\rm\implies{\bigg[ \bigg( \dfrac{1 + i7}{3} \bigg) + \bigg( \dfrac{12 + i1}{3} \bigg) \bigg] - \bigg( \dfrac{-4 + i3}{3} \bigg)}$

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$\rm\implies{\bigg[ \dfrac{1 + i7 + 12 + i1}{3} \bigg] - \bigg( \dfrac{-4 + i3}{3} \bigg)}$

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$\rm\implies{\bigg[ \dfrac{13 + i8}{3} \bigg] + \bigg( \dfrac{4 - i3}{3} \bigg)}$

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$\rm\implies{\dfrac{13 + i8 + 4 - i3}{3}}$

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$\rm\implies{\dfrac{17 + i5}{3}}$

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In the form of a + ib

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$\: \: \: \: \: \: \: \: \bullet\bf\: \: \: {\dfrac{17}{3} + i\dfrac{5}{3}}$