Express the complex numbers in the standard form a + ib: (3 – 4i) / [(4 – 2i) (1 + i)]

Question

Express the complex numbers in the standard form a + ib: \(\dfrac{ (3 – 4i) }{(4 – 2i) (1 + i)}\)

Asked by Aaryan | 1 year ago | 53

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Accepted Answer

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

\(\dfrac{ (3 – 4i) }{ (4 – 2i) (1 + i)}\)

= \(\dfrac{ (3-4i)}{4(1+i)-2i(1+i)}\)

= \(\dfrac{ (3-4i)}{(6+2i)}\)

[Multiply and divide with (6-2i)]

= \( \dfrac{ (3-4i)}{(6+2i)}×\dfrac{ (6-2i)}{(6-2i)}\)

= \( \dfrac{18 – 30i + 8 (-1) }{ (36 – 4 (-1))}\) [since, i²= -1]

=\( \dfrac{10-30i}{ 40}\)

=\(\dfrac{ (1 – 3i) }{ 4}\)

The values of a, b are \(\dfrac{ 1}{4}, \dfrac{-3}{4}\)

Answered by Aaryan | 1 year ago