1. Complex Numbers Arithmetic Operation Definition Complex Conjugate
History
History2
Equality
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2. Complex Numbers Polar Form Modulus & Argument Negative Argument
Arithmetic Operation
Power & Roots
DeMoivre’s theorem

3. z = a + ib Definition of Complex Numbers, z Imaginary part Real part
a = Re(z), b = Im(z)
Real part
example1
example2

4. Let z1 = a + ib and z2 = c + id Then, z1 + z2 = (a + c) + i(b + d) and
Addition and Subtraction of Complex Numbers
Let z1 = a + ib and z2 = c + id
Then,
z1 + z2 = (a + c) + i(b + d)
and
z1 - z2 = (a – c) + i(b – d)
example3

5. Let z1 = a + ib and z2 = c + id Then, z1z2 = (a + ib)x(c + id)
Multiplication of Complex Numbers
Let z1 = a + ib and z2 = c + id
Then,
z1z2 = (a + ib)x(c + id)
= (ac – bd) + i(ad + bc)
example4

6. Complex Conjugate
Given z = a + ib,
then its conjugate is
example5

7. Division of Complex Numbers
Let z1 = a + ib and z2 = c + id
example6