How do you simplify $(4-4i)/(5+3i)$ ?

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Answer 1 · 2015-11-21T00:11:10

$2/9-8/9i$

Use the conjugate of the denominator. (Recall that the conjugate of $a+b$ is $a-b$ .)

We can multiply the expression by $(5-3i)/(5-3i)$ .

$(4-4i)/(5+3i)((5-3i)/(5-3i))=(20-20i-12i+12i^2)/(25cancel(-15i+15i)-9i^2)=(20-32i+12i^2)/(25-9i^2)$

Recall that $i=sqrt1$ , so $i^2=-1$ .

$(20-32i+12(-1))/(25-9(-1))=(20-12-32i)/(25+9)=(8-32i)/36=2/9-8/9i$

Note that the answer is written in the complex number format $a+bi$ .

How do you simplify (4-4i)/(5+3i)(4-4i)/(5+3i)?