SOLUTION: Hi. Expressed in {{{a + bi}}} form, {{{5/(3 + i)}}} is equivalent to: A) {{{15 - 5i}}}, B) {{{3/2 - 1/2}}}{{{i}}}, C) {{{5/3 - 5i}}}, D) {{{15/8 - 5/8}}}{{{i}}}

Algebra ->  Radicals -> SOLUTION: Hi. Expressed in {{{a + bi}}} form, {{{5/(3 + i)}}} is equivalent to: A) {{{15 - 5i}}}, B) {{{3/2 - 1/2}}}{{{i}}}, C) {{{5/3 - 5i}}}, D) {{{15/8 - 5/8}}}{{{i}}}      Log On


   

Question 205028: Hi.
Expressed in a+%2B+bi form, 5%2F%283+%2B+i%29 is equivalent to:
A) 15+-+5i, B) 3%2F2+-+1%2F2i, C) 5%2F3+-+5i, D) 15%2F8+-+5%2F8i
Answer by Edwin McCravy(20054) About Me  (Show Source):
You can put this solution on YOUR website!
Expressed in a+%2B+bi form, 5%2F%283+%2B+i%29 is equivalent to:
A) 15 - 5i, B) (3/2) - (1/2i), C) (5/3) - 5i, D) (15/8) - (5/8i)

5%2F%28%283+%2B+i%29%29

Form the conjugate of the denominator by changing the
sign of the term containing i.  The conjugate of
%283%2Bi%29 is %283-i%29 so we multiply by the fraction
%28%283-i%29%29%2F%28%283-i%29%29 which just equals 1 and will not
change the value:

5%2F%28%283+%2B+i%29%29×%28%283-i%29%29%2F%28%283+-+i%29%29

Indicate the multiplication of the tops and bottoms:

%285%283-i%29%29%2F%28%283%2Bi%29%283-i%29%29

Distribute the top, FOIL out the denominator:

%285%283-i%29%29%2F%289-3i%2B3i-i%5E2%29

%285%283-i%29%29%2F%289-cross%283i%29%2Bcross%283i%29-i%5E2%29

%285%283-i%29%29%2F%289-i%5E2%29

Now we substitute %28-1%29 for i%5E2

%285%283-i%29%29%2F%289-%28-1%29%29

%285%283-i%29%29%2F%289%2B1%29

%285%283-i%29%29%2F10

%28cross%285%29%283-i%29%29%2Fcross%2810%5B2%5D%29

%283-i%29%2F2

Make two fractions:

3%2F2-i%2F2

Write i%2F2 as 1%2F2i

3%2F2-1%2F2i

Edwin