Download 3-2i) + - Houston ISD

DIVIDING
COMPLEX
NUMBERS
DO NOW
8i2
-2i -2i -8(-1) = -2i + 8
3. (3-2i) + (-5-9i)
-2 -11i
-10 + 35i +2i -7i2
-10 + 37i + 7 = -3 + 37i
4. (2 - 5i) - (-1 - 6i)
3 + 1i
Today’s Objective
IWBAT multiply and divide complex numbers
. . . And Why
To work with the square roots of negative
numbers
Dividing Complex Numbers

When we divide, we need to find the
Conjugate.
The complex numbers
&
are called complex conjugates
(They are EXACTLY the same
except for the + or -)
TRY THESE:
1.
-6 + 5i
2.
-6 – 5i
8 – i
8+i
3.
-9i
9i
3 + 2i
3 - 2i
Dividing Complex Numbers
To divide you must clear the
denominator of all i’s (called
“rationalizing”)
 To rationalize, multiply the
numerator and denominator by the
conjugate of the denominator

Quotient = Divide
Example 1:
Important:
What
happens if
The
product
of two
you
multiply
complex conjugates is
conjugates???
always a real number.
STEP 4:
DIVIDE
6
5 – 2i
Example #3
6
5 – 2i
Step 1:
Step 2:
Step 3:
Step4.
6(5 + 2i )
(5 – 2i )(5 + 2i )
 5 + 2i
5 + 2i
=
30 + 12i
=
25 +10i -10i -4(-1)2
30 + 12i
25 +4
= 30 + 12i
29
30 + 12 i
2
25 + 10 i – 10 i – 4i
Step 5: 30 + 12i
29 29
Example #4

Find the quotient (5+2i) and (4 - 3i)
5 + 2i
4 – 3i
5 + 2 i 4 + 3i

4 – 3 i 4 + 3i
(5 + 2i )(4 + 3i )
(4 – 3i )(4 + 3i )
2
20 + 15 i + 8 i + 6 i
2
16 – 12 i + 12 i – 9 i
20 + 23 i – 6
14 + 23 i or
=
16 + 9
25
14 + 23 i
25 25
Exit ticket answer key