Question

Evaluate 4x²-12x when x=(3/2)-(i/2).

Answer 1

-10

Explanation:

Let´s evaluate the complex number:

`4*((3)/(2) -(1)/(2)i)^(2) -12*((3)/(2) -(1)/(2)i)`

First let's calculate this expression:

`((3)/(2) -(1)/(2)i)^(2) =((3)/(2) -(1)/(2)i)*((3)/(2) -(1)/(2)i)`

Using distributive property:

`((3)/(2) )^(2) -2*((3)/(2)*(1)/(2)i )+((1)/(2)i )^(2)`

Where:

`i=√(-1)`

Therefore:

`2-(3)/(2) i`

Evaluating the rest of the expression using the distributive property again:

`4*(2-(3)/(2) i)-12*((3)/(2) -(1)/(2)i)=8-6i-18+6i=-10`