Complex numbers: simplify 100/(3 - 4i) into a + bi form

[thinker86]

Simplify the following complex number by writing it in the form a + bi where a and b are real numbers.

100/(3-4i)

I am completely stuck.

 

[stapel]

I am completely stuck.

Apply the "rationlizing the denominator" method they showed you in class. :wink:

Eliz.

 

[Deleted member 4993]

Simplify the following complex number by writing it in the form a + bi where a and b are real numbers.

100/(3-4i)

I am completely stuck.

\(\displaystyle \frac{a\, + \, ib}{c\, + \, id}\)

\(\displaystyle = \, \frac{a\, + \, ib}{c\, + \, id}\cdot\frac{c\, - \, id}{c\, - \, id}\)

\(\displaystyle =\, \frac{(ac \, + \, bd)\, + \, i(bc \, - ad)}{c^2\, + \, d^2}\)

\(\displaystyle =\, \frac{ac \, + \, bd}{c^2\, + \, d^2}\, + \, i\cdot \frac{bc \, - ad}{c^2\, + \, d^2}\)