Answer:
\(\frac{4}{-2-2i}=-1+i\)
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. \(\frac{4}{-2-2i}\)
We solve the expression by rationalization,
Rationalize by denominator,
\(=\frac{4}{-2-2i}\times \frac{-2+2i}{-2+2i}\)
Multiply, applying \((a+b)(a-b)=a^2-b^2\)
\(=\frac{4(-2+2i)}{(-2)^2-(2i)^2)}\)
\(=\frac{-8+8i}{4-4i^2}\)
\(=\frac{8(-1+i)}{4+4}\)
\(=\frac{8(-1+i)}{8}\)
\(=(-1+i)\)
Therefore, The solution is \(\frac{4}{-2-2i}=-1+i\)
