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

Asked by Aaryan | 1 year ago |  70

Solution :-

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

$$\dfrac{ (1 – i)^3 }{ (1 – i^3) }$$

=$$\dfrac{ [1 – 3i + 3(-1)-i^2.i] }{ (1 – (-1)i)}$$ [since, i= -1]

= $$\dfrac{-2-4i }{ (1+i)}$$

[Multiply and divide with (1-i)]

$$= \dfrac{-2-4i}{ (1+i)} × \dfrac{(1-i)}{(1-i)}$$

=$$\dfrac{ -2-2i+4(-1) }{2}$$

= $$\dfrac{ (-6-2i)}{2}$$

= -3 – i

The values of a, b are -3, -1

Answered by Aaryan | 1 year ago

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