find the quotient , write in standard form

Question

8+2i/4-8i

Answer 1

First, we can divide the numerator and denominator by 2 to get              

(4+i)/(2-4i)

 

Now, multiply the numerator and denominator by the conjugate of the denominator, 2+4i:

 

[(4+i)(2+4i)]/[(2-4i)(2+4i)] = [8+18i+4i²]/[4-16i²]  (NOTE:  i²=-1)

 

                                       = (4+18i)/20

 

                                       = (4/20) + (18/20)i = (1/5) + (9/10)i

 

 

Answer 2

To simplify the quotient of two complex numbers (EACH OF WHICH SHOULD HAVE HAD ITS OWN PAIR OF ENCLOSING PARENTHESES), multiply both numerator & denominator by the CONJUGATE of the denominator. This will produce a Real denominator, in the end, so that you get an answer in the form a + ib, with a & b most likely being rationals. Use FOIL for the multiplications & remember to replace i squared by -1.