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

Asked by Aaryan | 1 year ago |  70

1 Answer

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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