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Operations with Complex Numbers
Aim: Add, subtract, multiply and/or divide complex numbers in order to simplify.
Simplify:1. 2x + 3y – x + y
= x + 4y
2. (x + 3)(x – 3)
= x2 – 3x + 3x - 9
= x2 – 9
3.
( )
4. i2
Aim: Add, subtract, multiply and/or divide complex numbers in order to simplify.
Adding complex numbers
Find the sum of 4 + 2i and 2 – 5i.
Keep the real numbers together,
keep the imaginary numbers together.
is similar toadding polynomials.
Aim: Add, subtract, multiply and/or divide complex numbers in order to simplify.
4 + 2i + 2 - 5i 6 - 3i
Aim: Add, subtract, multiply and/or divide complex numbers in order to simplify.
Subtracting complex numbers
+− −( )
subtracting polynomials.
is similar to
Aim: Add, subtract, multiply and/or divide complex numbers in order to simplify.
Multiplying complex numbers is similar
to multiplying polynomials.
Aim: Add, subtract, multiply and/or divide complex numbers in order to simplify.
The complex conjugate
is similar to
the radical conjugate.
( )
Aim: Add, subtract, multiply and/or divide complex numbers in order to simplify.
Dividing complex numbers
is similar to
we just divided complex numbers.