Online Algebra Tutoring: Complex Numbers (Division)
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Learn Multiplication & Division of Complex Numbers from Certified Online Algebra Tutor
We use FOIL Method (which we use to multiply two binomials) to multiply two complex numbers.
F = Firsts
O = Outers
I = inners
L = Lasts
i = √-1, i2 = -1, i3 = – i, i4 = 1
p+qi and r+ti are two complex numbers.
(p+qi ) ×(r+ti) = pr + pti + qir + qti2
pr + (pt+qr) i + qti2
Example: (6 + 3i) × (3 + 4i)
= 18 + 24i + 9i + 12i2
= 18 + (24 + 9) i + 12(-1) ———— (because i2 = -1)
= 18 + 33i – 12
= 6+ 33
p+qi is a complex number. p-qi is the conjugate of p+qi. We can use conjugates to divide two Complex Numbers.
To divide two Complex Numbers, multiply numerator and denominator by the conjugate of the denominator.
The numerator and denominator can be solved by using FOIL.
(r+ti)×(r-ti) =r2-rti + rti-t2 i2
Example: (2+4i)÷ (3-4i)
Conjugate of 3 – 4i is 3 + 4i, so multiplying the numerator and denominator by this conjugate.
1. (3 – 3i) × (2 + 4i)
2. (6 – 3i)÷(2 + i)
3. (7 + 3i) ÷ (2 + 5i)
4. (4 + 5i) ÷ (3 + 2i)
5. (2 – 3i) × (4 + 7i)
It’s really magical!
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