Express the complex numbers in the standard form a + ib: (1 + 2i)-3

Asked by Sakshi | 1 year ago |  61

##### Solution :-

(1 + 2i)-3

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

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

= $$\dfrac{1}{(1+6i+4i^2+8i^3)}$$

=$$\dfrac{1}{(1+6i+4(-1)+8i^2.i)}$$ [since, i= -1]

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

[Multiply and divide with (3-2i)]

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

= $$\dfrac{ (-3+2i) }{ (9-4(-1))}$$

=$$\dfrac{ (-3+2i) }{13}$$

The values of a, b are $$\dfrac{ -3}{13}, \dfrac{2}{13}$$

Answered by Aaryan | 1 year ago

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