Question

Complex number in standard form. How do I do this?
5/(1+i)

Answer 1

is a+bi standard form?

if so you might want to run a conjugate

Answer 2

Yes

Answer 3

then a conjugate it is:

recall that (a+b)(a-b)=a^2-b^2

Answer 4

ok now what do i do?

Answer 5

essentially you mulitply by 1, but in the form of the conjugate ....

Answer 6

\[\frac{k}{a+b}*1\]
\[\frac{k}{a+b}*\frac{a-b}{a-b}\]
\[\frac{ka-kb}{a^2-b^2}\]
\[\frac{ka}{a^2-b^2}-\frac{kb}{a^2-b^2}\]

Answer 7

What is k?

Answer 8

It's just a general variable. Here's what you'll be doing. Take your denominator and flip the sign between the 1 and the i. This is your conjugate, in this case it's (1-i). Now multiply the numerator and denominator by (1+i)

Answer 9

(5-5i)/2

Answer 10

Right?

Answer 11

Right, exactly, so thats your answer: 2.5 - 2.5i

Answer 12

Thank you so much!

Answer 13

No problem, glad I could help