# Simplify the expression: (-10 - 5i) / (-6+6i)

Asked on by kentkeysert

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hala718 | High School Teacher | (Level 1) Educator Emeritus

Posted on

Let z= (-10-5i)/(-6+6i)

First we need to eliminate the complex denominator by multiplying by its inverse:

==> z= (-10-5i)(-6-6i)/(-6+6i)(-6-6i)

Let us simplify each:

(-10-5i)(-6-6i) = 60 + 60i + 30i + 30i^2

we know that i^2 = -1

==>                = 60 + 90i - 30

= 30 + 90i

(-6+6i)(-6-6i) = 36 + 36 = 72

==> z= (30 + 90i)/72

= (30/72)  + (90/72) i

= 5/12  + (5/4)i

==> z= (5/12) + (5/4) i

giorgiana1976 | College Teacher | (Level 3) Valedictorian

Posted on

We'll simplify (-10 - 5i) / (-6+6i) by multiplying the denominator by it's conjugate.

The conjugate of the - 6+6i = -6 - 6i

(-10 - 5i)*(-6-6i)/ (-6+6i)*(-6-6i)

We'll remove the brackets:

(60 + 60i + 30i - 30)/ (36 + 36)

We'll combine the real parts and the imaginary parts and we'll get:

(30 + 90i)/72

We'll factorize by 30 the numerator:

30(1 + 3i)/72 = 2.4(1 + 3i)

The simplified expression of:

(-10 - 5i) / (-6+6i) = 2.4 + 7.2i

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