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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.
The horizontal component is referred to as the real component, since that dimension is compatible with normal, scalar (“real”) numbers. The vertical component is referred to as the imaginary component, since that dimension lies in a different direction, totally alien to the scale of the real numbers. (Figure below )
Vector compass showing real and imaginary axes
The “real” axis of the graph corresponds to the familiar number line we saw earlier: the one with both positive and negative values on it. The “imaginary” axis of the graph corresponds to another number line situated at 90 ^{ o } to the “real” one. Vectors being two-dimensional things, we must have a two-dimensional “map” upon which to express them, thus the two number lines perpendicular to each other: (Figure below )
Vector compass with real and imaginary (“j”) number lines.
Either method of notation is valid for complex numbers. The primary reason for having two methods of notation is for ease of longhand calculation, rectangular form lending itself to addition and subtraction, and polar form lending itself to multiplication and division. Conversion between the two notational forms involves simple trigonometry. To convert from polar to rectangular, find the real component by multiplying the polar magnitude by the cosine of the angle, and the imaginary component by multiplying the polar magnitude by the sine of the angle. This may be understood more readily by drawing the quantities as sides of a right triangle, the hypotenuse of the triangle representing the vector itself (its length and angle with respect to the horizontal constituting the polar form), the horizontal and vertical sides representing the “real” and “imaginary” rectangular components, respectively: (Figure below )
Magnitude vector in terms of real (4) and imaginary (j3) components.
To convert from rectangular to polar, find the polar magnitude through the use of the Pythagorean Theorem (the polar magnitude is the hypotenuse of a right triangle, and the real and imaginary components are the adjacent and opposite sides, respectively), and the angle by taking the arctangent of the imaginary component divided by the real component:
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The STEREO SURROUNDeditioncontains all files from the STEREO edition plusthe samesounds in5.1 surround files. The tracklayout is: L • C • R • LFE • Ls • Rs
L • C • R • LFE • Ls • RsWe differentiate between sound FX and sound file. Each sound file can contain multiple variations of a sound (up to 6 variations based on the product). That way, we assure to provide you with different styles of a single sound in one file instead of multiple files, keeping your database nice and clear and speeding up your workflow as you have multiple variations available by dragging only one file to your audio host software.
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