Division of complex number
Now, we gave this formula a long with the comment that it will be convenient while it came to dividing complex numbers so let's look at a couple of examples.
Example Write down each of the following in standard form.
(3 - i)/(2+ 7i)
Solution
thus, in each case we are actually looking at the division of two complex numbers. However The main idea here is that we desire to write them in standard form. Standard form does not let for any i's to be in the denominator. Thus, we have to get the i's out of the denominator.
Actually this is fairly simple if we remember that a complex number times its conjugate is a real number. Thus, if we multiply the numerator & denominator by the conjugate of the denominator we will be capable to eliminate the i from the denominator.
(3 - i)/(2+ 7i) =(3 - i )( 2 - 7i)/ (2+ 7i) ( 2 - 7i) = 6 - 23i+ 7i^{2} /2^{2} +7^{2}
= -1 - 23i/53 = (1/53)-(23/53)i
Note that to put the answer into standard form we broke up the fraction into the real & imaginary parts.