Question

Find the value of x3 + x2 - x + 22 if x = 5 / 1 - 2i

Answer 1

Answer:

The required value is 7.

Step-by-step explanation:

Given,

$x=\frac{5}{1-2i}$

For removing imaginary number from the denominator,

Multiply both numerator and denominator by 1 + 2i,

$\implies x = \frac{5}{1-2i}\times \frac{1+2i}{1+2i}=\frac{5+10i}{1-4i^2}=\frac{5+10i}{1+4}=\frac{5+10i}{5}=1+2i$

$x^3 = (1+2i)^3 = 1 + 6i(1+2i) + 8i^3 = 1+ 6i + 12i^2 + 8i^3 = 1 + 6i - 12 -8i = -11-2i$

$x^2 = (1+2i)^2=1+4i+4i^2 = 1+4i-4=-3+4i$

$\implies x^3 + x^2 - x + 22=-11-2i-3+4i-1-2i+22=7$