Answer:
-10
Step-by-step explanation:
Let´s evaluate the complex number:
[tex]4*(\frac{3}{2} -\frac{1}{2}i)^{2} -12*(\frac{3}{2} -\frac{1}{2}i)[/tex]
First let's calculate this expression:
[tex](\frac{3}{2} -\frac{1}{2}i)^{2} =(\frac{3}{2} -\frac{1}{2}i)*(\frac{3}{2} -\frac{1}{2}i)[/tex]
Using distributive property:
[tex](\frac{3}{2} )^{2} -2*(\frac{3}{2}*\frac{1}{2}i )+(\frac{1}{2}i )^{2}[/tex]
Where:
[tex]i=\sqrt{-1}[/tex]
Therefore:
[tex]2-\frac{3}{2} i[/tex]
Evaluating the rest of the expression using the distributive property again:
[tex]4*(2-\frac{3}{2} i)-12*(\frac{3}{2} -\frac{1}{2}i)=8-6i-18+6i=-10[/tex]
