Question

When solving inequality

Answer 1

Answer:

we need to factorise if imaginary number is in the denominator. no action is required if its in the numerator.

you can factorise an imaginary number by multiplying both the numerator and denominator by the conjuncate of the complex number

for instance,

we've given a complex number as follows

$\frac{x}{3x + 4i}$

factorising

$\frac{x}{3x + 4i} \times \frac{3x - 4i}{3x - 4i}$

as 3x -4i is the conjugate of 3x + 4i

and 4i is the imaginary number

$\frac{ x(3x - 4i)}{9x {}^{2} - 4 {i}^{2} }$

and since i² = -1

$\frac{ x(3x - 4i)}{9x {}^{2} + 4}$

hence factorised