How do you simplify $(2+2i)/(1+2i)$ and write in a+bi form?

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Answer 1 · 2015-12-11T00:49:06

Multiply the numerator and denominator by the complex conjugate of the denominator to find

$(2+2i)/(1+2i)=6/5 - 2/5i$

Given a complex number $a+bi$ with $a,b in RR$ we have

$(a+bi)(a-bi) = a^2 + b^2$

$a-bi$ is called the complex conjugate (or conjugate) of $a+bi$ . Using this:

$(2+2i)/(1+2i) = (2+2i)/(1+2i)*(1-2i)/(1-2i)$

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

$= (6-2i)/5$

$=6/5 - 2/5i$

How do you simplify (2+2i)/(1+2i) (2+2i)/(1+2i) and write in a+bi form?