Consider two complex numbers z1, z2
z1 = a1 + ib1
z2 = a2 + ib2
Multiplying the numerator and denominator by the complex conjugate of z2, that is
= a2 - ib2
we obtain
Example 1
Divide 4 - 6i by 2 - 3i
Let z1 = 4 - 6i, a1 = 4, b1 = -6
z2 = 2 - 3i, a2 = 2, b2 = -3
Example 2
Divide 7i - 5 by 10 + 2i
Let z1 = 7i-5, a1 = -5, b1 = 7
z2 = 10+ 2i, a2 = 10, b2 = 2
Comparing with
Example 3
Divide -12-5i by 1-4i
Let Z1 =-12-5i a1 = -12 b1 = -5
Z2 = 1+ 4i a2 = 1 b2 = -4
Example 4
Divide -1 -i by -2-4i
Let z1 = -1 -i, a1 = -1 b1 = -1
z2 = -2- 4i, a2 = -2, b2 = -4
Try these questions
Divide the following complex numbers
-
Divide 8 + 3i by 5 + 6i
Answer: let z1 = 8+3i, a1 = 8, b1 = 3
z2 = 5+6i, a2 = 5, b2 = 6
Comparing with
- Divide -3 + 4i by 10-2i
Answer: Let z1 = -3+4i, a1=-3, b1=4
z2=10-2i, a2=10, b2=-2
-
Divide -1 -i by (-4 -3i )
Answer: Let z1 =-1-i a1=-1, b1=-1
z2 =-4-3i a2= -4, b2=-3
-
Divide 12i by 3 - 4i
Answer: Let z1 = 12i = 0+12i, a1= 0, b1= 12
z2 =-3-4i, a2=3, b2=-4
-
Divide -5 by 7 + 5i
Answer: Let z1 = -5 + 0i a1= -5, b1= 0
z2 = 5 + 6i a2= 5, b2= 6
-
Divide 9 + 11i by 2
Answer: Let z1 =9+11i a1=9 b1=11
z2 = 2=2+0i a2=2 b2=0
On reducing to the lowest terms for each fraction
-
Divide (-3 -18i ) by 12i
Answer: Let z1 = -3-18i a1=-3 b1= -18
z2 = 12i =0+12i a2=0 b2=12
-
Divide 4 - 6i by 4 + 6i
Answer: Let z1 = 4 - 6i a1= 4 b1= -0
z2 = 4 + 6i a2= 4 b2= 6
On reducing each fraction to the lowest term
-
Divide -5 -12i by -5 +12i
Answer: Let z1 =-5- 12i a1=-5 b1=-12
z2 =-5 + 12i a2=-5 b2=12
On reducing to the lowest terms for each fraction