Download Division of complex numbers notes 1

LEARNING TARGET:
What is a complex Conjugate?
Complex Conjugates: for any complex number 𝑎 + 𝑏𝑖 there is a complex conjugate
_______________
Example: 3 + 7𝑖 and 3 − 7𝑖 are complex conjugates
Name the conjugate of the following complex numbers:
a.) 6 + 3𝑖
b.) 10 − 4𝑖
c.) −𝑖
How do I divide Complex Numbers?
Dividing Complex Numbers
Just like with radicals, we don’t want imaginary numbers in the denominator. We have to fix
that.
Multiply the top and bottom of the fraction by the __________________ of the
_______________________.
How do I solve these problems?
Examples:
a.)
5+3𝑖
To solve the problem, I will start by multiplying it with the numerator
and the denominator with the ______________ of the denominator.
1−2𝑖
The conjugate of 1 − 2𝑖 is 1 +
2
numerator
5+3𝑖
×
Éiy
1−2𝑖
=
on
STEPI
Lookfor the
contuaateor
Denominator
=
=
b.)
2−7𝑖
1+𝑖
2−7𝑖
1+𝑖
×
=
simplify
=
=
c.)
3+11𝑖
3+11𝑖
−1−2𝑖
−1−2𝑖
×
=
=
=
(
)(
)
(
)(
)
simplify