Question

5)
Find the value of
iii) x3 – x2+x+46, if x = 2+3i.​

Answer 1

Here i is not possible so let

x=2+3

x=5

then answer is

Answer 2

Answer:

The value of the expression is $x^3-x^2+x+46=7$, if $x=2+3i$.                              

Step-by-step explanation:

To find : The value of $x^3-x^2+x+46$ ,If $x=2+3i$?

Solution :

First we find the values in parts,

$x=2+3i$ ....(1)

Squaring both side,

$x^2=(2+3i)^2$

$x^2=2^2+(3i)^2+2\times 2\times 3i$

$x^2=4-9+12i$

$x^2=-5+12i$  .....(2)

Multiply (1) and (2),

$x\times x^2=(2+3i)(-5+12i)$

$x^3=-10+24i-15i+36i^2$

$x^3=-10+9i-36$

$x^3=-46+9i$ .....(3)

Substitute all (1),(2) and (3) in the equation,

$x^3-x^2+x+46$

$=-46+9i-(-5+12i)+2+3i+46$

$=-46+9i+5-12i+2+3i+46$

$=7+0i$

$=7$

Therefore, The value of the expression is $x^3-x^2+x+46=7$, if $x=2+3i$.