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

Asked by Aaryan | 1 year ago |  53

##### Solution :-

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, i= -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

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