Learning Objective

Reading

Complex Analysis

explanations of j

Convenient examples

Basic math

Addition and subtraction

Example | (pdf)

Multiplication

Rationalization

Example 1 | (pdf)

Example 2 | (pdf)

Conjugate

Definition | (pdf)

Example 1 | (pdf)

Example 2 | (pdf)

Example 3 | (pdf)

Magnitude

Example 1 | (pdf)

Phase

Re[]

Example 1 | (pdf)

Example 2 | (pdf)

Im[]

Roots and Powers

Nth roots

example | (pdf)

Nth roots of unity

Powers

example | (pdf)

Rect and Polar Forms

Euler's formula (complex exp)

Polar form

Rect<->polar xform triangle

Example 1 | (pdf)

Example 2 | (pdf)

Example | (pdf)

4.1    Perform these operations on complex numbers:

          a.   Multiply, divide, add, and subtract complex numbers.

          b.   Find the complex conjugate of any complex number.

          c.   Rationalize the denominator of a fraction of complex numbers.

          d.   Convert from polar form to rectangular form and vice versa.

          e.   Find the real part of any complex number.

          f.    Find the absolute value (i.e., magnitude) of any complex number.

          g.   Find the nth root or power of any complex number.

App B

Complex Analysis

Phasors

Tutorial | (pdf)

Rotating stick shadow

Identities

Phasor math

Phasor<->inv-phasor xform

Example 1 | (pdf)

Example 1 (cont) (pdf)

Example 2 | (pdf)

Example 2 (cont) (pdf)

4.2    Take the phasor transform of a sinusoidal function of time and inverse phasor transform of a phasor.

Chap 9:

Sec 9.1-9.3

Impedance circuits

Ohm's law

Statement

Series impedances

Parallel impedances

Impedance networks

Example 1 (pdf)

Example 2 (pdf)

4.3    Transform circuits to the frequency domain and apply the concept of impedance in the frequency domain. This includes finding the equivalent impedance of combinations of elements.

Chap 9:

Sec 9.4,9.6

Impedance circuits

Kirchhoff's laws

Example (pdf)

4.4    Apply Kirchhoff's laws in the frequency domain.

Chap 9:

Sec 9.5

Impedance circuits

Node-voltage method

Example (pdf)

4.5    Apply the node-voltage method in the frequency domain.

Chap 9:

Sec 9.8

Impedance circuits

Mesh-current method

Example (pdf)

4.6    Apply the mesh-current method in the frequency domain.

Chap 9:

Sec 9.9

Impedance circuits

Thevenin equivalent

Deriving Thevenin equivalent

Example 1 (pdf)

Example 2 (pdf)

4.7    In the frequency domain, transform sources and find Thevenin and Norton equivalent circuits.

Chap 9:

Sec 9.7

Superposition

Circuits

VAC + VAC

Example (pdf)

4.8    Apply the principle of superposition in the frequency domain.

Complex Analysis

Phasors

Phasor diagrams

Example (pdf)

4.9    Draw appropriate phasor diagrams and use them in analyzing and designing circuits.

Chap 9:

Sec 9.12