SOLUTION: It says to write each quotient in the form of a + bi Don't know how The problem is 3i/-2+i

Algebra ->  Complex Numbers Imaginary Numbers Solvers and Lesson -> SOLUTION: It says to write each quotient in the form of a + bi Don't know how The problem is 3i/-2+i      Log On


   

Question 208350This question is from textbook College Algebra
: It says to write each quotient in the form of a + bi
Don't know how
The problem is 3i/-2+i This question is from textbook College Algebra

Answer by Edwin McCravy(20054) About Me  (Show Source):
You can put this solution on YOUR website!
It says to write each quotient in the form of a+%2B+bi
Don't know how
The problem is %283i%29%2F%28-2%2Bi%29
 
Put parentheses around it:

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

Multiply by %28%28-2-i%29%2F%28-2-i%29%29

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

Indicate the multiplications of tops and bottoms:

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

Ditribute on top,  FOIL on bottom:

%28-6i-3i%5E2%29%2F%284%2B2i-2i-i%5E2%29

The middle two terms cancel in the bottom:

%28-6i-3i%5E2%29%2F%284%2Bcross%282i%29-cross%282i%29-i%5E2%29

%28-6i-3i%5E2%29%2F%284-i%5E2%29

Replace both i%5E2 terms by -1

%28-6i-3%28-1%29%29%2F%284-%28-1%29%29

%28-6i%2B3%29%2F%284%2B1%29%29

%28-6i%2B3%29%2F5%29

Make two fractions:

-6i%2F5%2B3%2F5

Write the term with i second:

3%2F5-6i%2F5

Write the second term %28-6i%29%2F5 as -6%2F5i, so
it will be in the form "bi"

3%2F5-6%2F5i

Edwin