Now lets divide complex numbers Whoohooo To divide

Now lets divide complex numbers Whoohooo!!!!

To divide by a complex number means a complex number will be in the denominator. (cause division can be represented as a fraction). So we will multiply the numerator and the denominator by the complex conjugate of the denominator…. So here goes: Helpful Hint The complex conjugate of a complex number a + bi is a – bi. (Lesson 5 -5)

Example 7 A: Dividing Complex Numbers Simplify. Multiply by the conjugate. N is (3+10 i)(-5 i) so distrib. Distribute.

Use i 2 = – 1. so (-50)(-1) = +50 Now you are breaking up the fraction b writing each term of N over the D

Example 7 B: Dividing Complex Numbers Simplify. Multiply N and D by the conjugate of D. You will have to foil N and D: N: (2+8 i)(4+2 i) becomes D: (4 -2 i)(4 + 2 i) becomes 2(4+2 i) +8 i(4+2 i) 4(4+2 i) -2 i(4+2 i) 2 2 8 +4 i + 32 i +16 i note: i = -1 16 + 8 i -4 i 2 8 + 4 i + 32 i + 16(-1) 16 + 0 -4(-1) 8 + 4 i + 32 i - 16 20 -8 + 36 i 16 + 4

So now N over D gives you the following: To write it as a complex number break the N up by writing each term over the D Now reduce each fraction rewrite with proper form of complex number

Check It Out! Example 7 a Simplify. Multiply by the conjugate. Distribute. Use i 2 = – 1. Simplify.

Check It Out! Example 7 b Simplify. Multiply by the conjugate. Distribute. Use i 2 = – 1 and simplify. Write in proper complex number form