Answer:
[tex]\frac{4}{-2-2i}=-1+i[/tex]
Step-by-step explanation:
Given : Expression 4 over the quantity of negative 2 minus 2i.
To find : Simplify the expression ?
Solution :
Re-write the expression as
4 over the quantity of negative 2 minus 2i i.e. [tex]\frac{4}{-2-2i}[/tex]
We solve the expression by rationalization,
Rationalize by denominator,
[tex]=\frac{4}{-2-2i}\times \frac{-2+2i}{-2+2i}[/tex]
Multiply, applying [tex](a+b)(a-b)=a^2-b^2[/tex]
[tex]=\frac{4(-2+2i)}{(-2)^2-(2i)^2)}[/tex]
[tex]=\frac{-8+8i}{4-4i^2}[/tex]
[tex]=\frac{8(-1+i)}{4+4}[/tex]
[tex]=\frac{8(-1+i)}{8}[/tex]
[tex]=(-1+i)[/tex]
Therefore, The solution is [tex]\frac{4}{-2-2i}=-1+i[/tex]
