Form of a complex number:

(F.1)

(F.2)

(F.3)

Conversion from the polar form to the rectangular form:

(F.4)

Conversion from the rectangular form to the polar form:

(F.5)

We usually specify the principal value of the angle such that ?180 < ? ? 180 . The angle value can be determined as:

(that is, the complex number is in the first or fourth quadrant in the rectangular coordinate system);

(that is, the complex number is in the second quadrant in the rectangular coordinate system); and

(that is, the complex number is in the third quadrant in the rectangular coordinate system). Note that

Complex numbers:

(F.6)

(F.7)

(F.8)

Complex conjugate of a + jb:

(F.9)

Complex conjugate of Ae ^j?:

(F.10)

Complex number addition and subtraction:

(F.11)

Complex number multiplication:

Rectangular form:

(F.12)

(F.13)

Polar form:

(F.14)

Complex number division:

Rectangular form:

(F.15)

Polar form:

(F.16)

Trigonometric identities:

(F.17)

(F.18)

(F 19)

(F.20)

(F.21)

(F.22)

(E.23)

(F.24)

(F.25)

(F.26)

(F.27)

(F.28)

(F.29)

Series of exponentials:

(F.30)

(F.31)

(F.32)

(F.33)

L'Hospital's rule:

If results in the undetermined form or , then,

(F.34)

where and .

Solution of the quadratic equation:

For a quadratic equation expressed as

(F.35)

the solution is given by

(F.36)