Difference between real and Imginary components As a complete complex number, the horizontal and vertical quantities are written as a sum: (Figure below) In “rectangular” form the vector’s length and direction are denoted in terms of its horizontal and vertical span, the first number representing the the horizontal (“real”) and the second number (with the “j” prefix) representing the vertical (“imaginary”) dimensions. 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. 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 two dimensional figures (horizontal and vertical) are symbolized by two numerical figures. 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.”
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. The Rectangular form, on the other hand, is where a complex number is denoted by its respective horizontal and vertical components. The vector compass What is Rectangular Form (Figure below) The above vector on the right (7.81 ∠ 230.19 o) can also be denoted as 7.81 ∠ -129.81 o. For example, a vector angled ∠ 270 o (straight down) can also be said to have an angle of -90 o.
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. 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. 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. The 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: ∠).
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