Question

Question #a2849

Answer 1

`2/5`

Explanation:

For this problem, I'm going to work under the assumption that you were asking to simplify the expression `(2-2i)/(5-5i)`.

To simplify complex division problems, you must use the concept known as the complex conjugate. For a complex number written in the format `a+bi`, the complex conjugate is the expression `a-bi`.

To simplify the division, you will multiply the numerator and denominator of the original expression by the complex conjugate of the denominator. You then use the properties of the imaginary unit `i` to reduce and simplify the resulting expressions.

`(2-2i)/(5-5i) = (2-2i)/(5-5i) * (5+5i)/(5+5i) = ((2-2i)(5+5i))/((5-5i)(5+5i))`

`= (10 + 10i -10i -10i^2)/(25+25i-25i-25i^2) = (10-10i^2)/(25-25i^2)`

`= (10-10(-1))/(25-25(-1)) = (10+10)/(25+25) = 20/50 = 2/5`