Take the 2-minute tour ×
Mathematics Stack Exchange is a question and answer site for people studying math at any level and professionals in related fields. It's 100% free, no registration required.

I know this is so simple but my algebra is totally failing me.. I have the equation 1/1+2i and I want to extract the real and imaginary parts so I have it in the form..

Re+Im could someone just show me the algebra steps for doing this please.. Thanks

share|improve this question
    
$\dfrac{1}{1+2i} = \dfrac{1-2i}{(1+2i)(1-2i)} = \ldots$. –  njguliyev Oct 31 '13 at 11:00
add comment

1 Answer

up vote 0 down vote accepted

Multiply by the conjugate: $$ \frac{1}{1+2i}=\frac{1}{1+2i}\cdot \frac{1-2i}{1-2i}=\frac{1-2i}{5}. $$

share|improve this answer
    
Being a non-native speaker: shouldn't it be called “expand with” instead of “multiply by”? –  Michael Hoppe Oct 31 '13 at 11:05
    
@MichaelHoppe I use "multiply" because I am multiplying two complex numbers together. –  Joe Johnson 126 Oct 31 '13 at 11:25
1  
But you didn't multiply by the conjugate but with $1$ instead ... Just nitpicking –  Michael Hoppe Oct 31 '13 at 11:51
    
@MichaelHoppe I multiplied by the conjugate twice, once on top and once on bottom. So, I did multiply by the conjugate. –  Joe Johnson 126 Oct 31 '13 at 15:44
    
OK, but what is the proper verb for “to multiply the nominator and the denominator of a fraction by the same number“? It's called “erweitern” in german and I presumed that the english verb is “to expand by.” In case you multiply a fraction by a number you'll multiply the nominator of the fraction by this number and leave the denominator unchanged. –  Michael Hoppe Oct 31 '13 at 15:56
show 2 more comments

Your Answer

 
discard

By posting your answer, you agree to the privacy policy and terms of service.

Not the answer you're looking for? Browse other questions tagged or ask your own question.