# Simplify the expression (-12-6i)/(-6+6i)?

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The expression to be simplified is (-12-6i)/(-6+6i)

(-12-6i)/(-6+6i)

cancel the common factor -6

=> (2 + i)/( i - 1)

=> (2 + i)(i +1) / (i - 1)(i + 1)

=> 2i + 2 + i^2 + i)/2

=> (3i + 1)/2

=> (3/2)i + 1/2

**The simplified form of the expression is (1/2) + (3/2)i**

First, we'll factorize both numerator and denominator by -6

-6(2 + i)/-6(1 - i) = (2+i)/(1-i)

We'll simplify (2+i)/(1-i)by multiplying the denominator by it's conjugate.

The conjugate of the 1 - i = 1 + i

(2+i)(1+i)/(1-i)(1+i)

We'll remove the brackets:

(2 + 2i + i + i^2)/ (1-i^2)

We'll combine the real parts and the imaginary parts, considering i^2 = -1, and we'll get:

(1 + 3i)/2

**The simplified expression is: (-12 - 6i) / (-6+6i) =1/2+ 3i/2**