1. ECE 1304 Introduction to Electrical and Computer Engineering
Section 1.4
Complex Arithmetic in MATLAB 1

2. Complex Arithmetic
MATLAB performs all complex number operations automatically.
Complex numbers must include the real and imaginary parts.
>> z = a + bj or
>> z = a + bi

3. Complex Numbers
Note the answer is in the form
z = a + bi

4. Complex Number Addition
(a + jb) + (c + jd) = (a + c) + j(b + d)

5. Complex Number Multiplication
(a + jb)(c + jd) = ac – bd + j(ad + bc)

6. Complex Number Division

7. Complex Numbers Polar Form z = r cos() + j r sin() z = a + jb r b 
Real Axis
Imaginary Axis
z = r cos() + j r sin() a b
z = a + jb r 

8. Absolute Value (Magnitude)

9. Angle (Phase Angle)

10. Polynomial Equations Any polynomial equation such as ax2 + bx + c = 0
may be represented by a vector of the coefficients
v = [a b c]
This is applicable to polynomials of any degree
v = [ ]
represents
3x4 + 6x3 + x2 + 7x + 2 = 0

11. Polynomial Roots The roots of the quadratic equation 2x2 + x + 1 = 0
is easily found

12. Polynomial Roots The 4th order polynomial equation
3x4 + 6x3 + x2 + 7x + 2 = 0
has the roots