Question

Evaluate 4x²-12x when x=(3/2)-(i/2).

Answer 1

Answer:

-10

Step-by-step explanation:

Let´s evaluate the complex number:

$4*(\frac{3}{2} -\frac{1}{2}i)^{2} -12*(\frac{3}{2} -\frac{1}{2}i)$

First let's calculate this expression:

$(\frac{3}{2} -\frac{1}{2}i)^{2} =(\frac{3}{2} -\frac{1}{2}i)*(\frac{3}{2} -\frac{1}{2}i)$

Using distributive property:

$(\frac{3}{2} )^{2} -2*(\frac{3}{2}*\frac{1}{2}i )+(\frac{1}{2}i )^{2}$

Where:

$i=\sqrt{-1}$

Therefore:

$2-\frac{3}{2} i$

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

$4*(2-\frac{3}{2} i)-12*(\frac{3}{2} -\frac{1}{2}i)=8-6i-18+6i=-10$