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

Asked by Aaryan | 1 year ago |  67

##### Solution :-

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

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

= $$\dfrac{ (2 + 11i) }{ (2 + 3i)}$$

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

=$$\dfrac{ (2 + 11i)}{(2 + 3i)} × \dfrac{(2-3i)}{(2-3i)}$$

= $$\dfrac{ (4 + 16i – 33(-1)) }{ (4 – 9(-1))}$$ [since, i= -1]

= $$\dfrac{ (37 + 16i) }{ 13}$$

The values of a, b are $$\dfrac{ 37}{13}, \dfrac{16}{13}$$

Answered by Aaryan | 1 year ago

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