Question

Represent:
1+7i/(2-i)²
in a + ib form. Where i = √-1

Answer 1

$\sf\dfrac{1+7i}{(2-i)^{2}}$

= $\sf\dfrac{1+7i}{(2)^{2} + (i)^{2} - 2 × 2 × i}$

= $\sf\dfrac{1+7i}{4 + (-1) - 4i}$

= $\sf\dfrac{1+7i}{3 - 4i}$

By rationalising it,

= (1+7i)/(3-4i) × (3+4i)/(3+4i)

= (1+7i)(3+4i)/(3)² - (4i)²

= (3 + 4i + 21i + 28i²)/ 9 + 4

= (3 + 25i - 28)/13

= (-25 + 25i)/13

= (-25/13) + (25i/13) is the a + ib form

where, a = (-25/13) and b = (25/13).