Express the complex numbers in the standard form a + ib : $$\dfrac{(1 + i) (1 +\sqrt{3i})}{ (1 – i)}$$

Asked by Aaryan | 1 year ago |  53

##### Solution :-

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

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 ago

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