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In order to work with these complex numbers without drawing vectors, we first need some kind of standard mathematical notation. There are two basic forms of complex number notation: polar and rectangular .

Polar form is where a complex number is denoted by the length (otherwise known as the magnitude , absolute value , or modulus ) and the angle of its vector (usually denoted by an angle symbol that looks like this: ∠). To use the map analogy, polar notation for the vector from New York City to San Diego would be something like “2400 miles, southwest.” Here are two examples of vectors and their polar notations: (Figure below )

Vectors with polar notations.

Standard orientation for vector angles in AC circuit calculations defines 0 o as being to the right (horizontal), making 90 o straight up, 180 o to the left, and 270 o straight down. Please note that vectors angled “down” can have angles represented in polar form as positive numbers in excess of 180, or negative numbers less than 180. For example, a vector angled ∠ 270 o (straight down) can also be said to have an angle of -90 o . (Figure below ) The above vector on the right (7.81 ∠ 230.19 o ) can also be denoted as 7.81 ∠ -129.81 o .

The vector compass

Rectangular form, on the other hand, is where a complex number is denoted by its respective horizontal and vertical components. In essence, the angled vector is taken to be the hypotenuse of a right triangle, described by the lengths of the adjacent and opposite sides. Rather than describing a vector’s length and direction by denoting magnitude and angle, it is described in terms of “how far left/right” and “how far up/down.”

These two dimensional figures (horizontal and vertical) are symbolized by two numerical figures. In order to distinguish the horizontal and vertical dimensions from each other, the vertical is prefixed with a lower-case “i” (in pure mathematics) or “j” (in electronics). These lower-case letters do not represent a physical variable (such as instantaneous current, also symbolized by a lower-case letter “i”), but rather are mathematical operators used to distinguish the vector’s vertical component from its horizontal component. As a complete complex number, the horizontal and vertical quantities are written as a sum: (Figure below )

Thursday Forum

Coe College invites you to participate in the Thursday Forum, a program for adults who want to extend their knowledge in an academic setting.

Most Thursday Forum lectures are held in Kesler Lecture Hall of Hickok Hall on the Coe campus.

Each session begins with registration and refreshments from 8:45-9:15 a.m., followed by the class until 11:30 a.m. The class meetings blend lecture, media such as film and music, and discussion. An optional luncheon is offered at the conclusion of the series.

Admission to the entire four-week course can be purchased for $35 on the first day or in advance. Admission to the individual lectures is $12 per week. The closing luncheons cost an additional $8.

Payment can be made in personon Thursdaymornings by cash or personal check. Credit card payments can be processed online only. Clickhere to pay by credit card or directly from your checking account .To order gift certificates, call 319-399-8523.

Clickhere to pay by credit card or directly from your checking account

In the event of inclement weather, consult local media outlets to find out if the day's Thursday Forum will take place.

Thursday Forum participants may park for free in any Coe parking lots, provided spaces are available. Given the high demand for on-campus parking, you may want to consider carpooling or public transportation.

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