Question 120862This question is from textbook College Algebra
: Evaluate the expression and write the result in the form a + bi.
1/8+10i - 1/8+10i = _____ + _______i
I do not know how to divide complex numbers. Note that that 8+10i is the numerator in both equations.
I would greatly appreciate your help!! Thank you so much.
This question is from textbook College Algebra
Found 2 solutions by checkley71, solver91311:
Answer by checkley71(8403)   (Show Source):
You can put this solution on YOUR website! I'LL ASSUME YOU MEAN THE (8+10i) IS IN THE DENOMINATOR!!!!!
1/(8+10i)-1/(8+10i)
(8+10i)-(8+10i)/(8+10i)(8+10i)
8-8+10i-10i/(8+10i)(8+10i)
0+0/(8+10i)(8+10i)=0 ANSWER.
Answer by solver91311(24713)  (Show Source):
You can put this solution on YOUR website! I'm pretty sure you meant to say 8 + 10i is the denominator of both fractions, and your problem actually looks like:
Just like working with any other fractions, if the denominators are equal, then you simply add the numerators.
We could have made this a little more complicated by using a process called rationalizing the denominators, but the result will still be the same. Watch closely.
First thing is to remember that  . Having said that, we are now going to multiply each of the fractions by 1, in the form of  :
 (remember that  ), so our denominator becomes 164, giving us:
Now, to add complex numbers, you just add the real parts to the real parts and the imaginary parts to the imaginary parts: 
In our problem, we have  giving us:
If you need to express 0 in complex number ( ) form, then you would write  .
Hope that helps.
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