\( \dfrac{(1 + i) (1 +\sqrt{3i})}{ (1 – i)}\)

Let us simplify and express in the standard form of (a + ib),

= \( \dfrac{1(1+\sqrt{3i}) + i(1+\sqrt{3i})}{(1-i)}\)

= \( \dfrac{ (1 + \sqrt{3i} + i + \sqrt{3i^2})}{(1 – i)}\)

=\( \dfrac{(1-\sqrt{3}) + (1+\sqrt{3})i}{(1-i)}\)

[multiply and divide with (1+i)]

=\( \dfrac{(1-\sqrt{3}) + (1+\sqrt{3})i}{\dfrac{ (1-i) × (1+i)}{(1+i)}}\)

= \( -\sqrt{3} + i\)

The values of a, b are \( -\sqrt{3} ,1\)

Answered by Aaryan | 1 year agoShow that 1 + i^{10} + i^{20} + i^{30} is a real number?

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