### Review of Complex Numbers

A complex number is made up of two parts: a real part and an imaginary part. A complex number can be represented by an ordered pair (a,b), where a is the value of the real part of the number and b is the value of the imaginary part. If (a,b) and (c,d) are complex numbers, then the following statements are true:

- (a,b) + (c,d) = (a+c,b+d)
- (a,b) - (c,d) = (a-c,b-d)
- (a,b) * (c,d) = (ac-bd,ad+bc)
- (a,b) / (c,d) = ((ac+bd) / (c²+d²), (bc-ad) / (c²+d²))
- The conjugate of a complex number (a,b) is (a,-b)
- The absolute value or magnitude of a complex number (a,b) is the positive square root of the value a² + b²
- The polar representation of (a,b) is (r,theta), where r is the distance from the origin to the point (a,b) in the complex plane, and theta is the angle from the real axis to the vector (a,b) in the complex plane. The angle theta can be positive or negative. The following figure illustrates the polar representation (r,theta) of the complex number (a,b).