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== Complex Numbers == | == Complex Numbers == | ||
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Complex numbers are very important for mathmeticians and engineers alike. However, the two use slightly different terminologies. Mathmeticians use "i" to denote an imaginary number, but electrical engineers use "j" to symbolize an imaginary number since "i" is used for current (specifically electron current since its a lower case "i"). | Complex numbers are very important for mathmeticians and engineers alike. However, the two use slightly different terminologies. Mathmeticians use "i" to denote an imaginary number, but electrical engineers use "j" to symbolize an imaginary number since "i" is used for current (specifically electron current since its a lower case "i"). | ||
As denoted below, "j" represents a -1 inside of a square-root. All complex numbers can be broken down into both a real part and an imaginary part. These two parts are best explained using graphical representation. The x-axis is the real part of the number. The y-axis represents the imaginary axis. | As denoted below, "j" represents a -1 inside of a square-root. All complex numbers can be broken down into both a real part and an imaginary part. These two parts are best explained using graphical representation. The x-axis is the real part of the number. The y-axis represents the imaginary axis. | ||
| − | + | <pre> | |
IMAGINARY | IMAGINARY | ||
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| − | ''' | + | </pre> |
| + | '''Euler's Formula: | ||
| + | <math>e^{jt} = [cos(t) + j*sin(t)], | ||
| + | j=\sqrt(-1) </math>''' | ||
| + | |||
| + | Q1. What is the real part of <math>e^{2pi*jt}</math>? Is there an imaginary part? | ||
| + | |||
| + | Q2. Solve <math>Ce^{x*jt} = 3j</math> for C and x. | ||
| + | |||
| + | Q3. Solve <math>Ce^{x*jt} = 5</math> for C and x. | ||
| + | |||
| + | Q4. True or False, 3j+6j*4j = -24 + 3j | ||
| + | |||
| − | + | <pre> | |
| + | Answers: Q1.) Real part = 1, Imaginary Part = 0 | ||
| + | Q2.) C = 3, x = pi/2 | ||
| + | Q3.) C = 5, x = 0 | ||
| + | Q4.) True | ||
| + | </pre> | ||
Latest revision as of 05:20, 5 September 2008
Complex Numbers
Complex numbers are very important for mathmeticians and engineers alike. However, the two use slightly different terminologies. Mathmeticians use "i" to denote an imaginary number, but electrical engineers use "j" to symbolize an imaginary number since "i" is used for current (specifically electron current since its a lower case "i").
As denoted below, "j" represents a -1 inside of a square-root. All complex numbers can be broken down into both a real part and an imaginary part. These two parts are best explained using graphical representation. The x-axis is the real part of the number. The y-axis represents the imaginary axis.
IMAGINARY
| .
| /.
| / .
| / .
| / .
| / .
___|/_____.__REAL
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|
Euler's Formula: $ e^{jt} = [cos(t) + j*sin(t)], j=\sqrt(-1) $
Q1. What is the real part of $ e^{2pi*jt} $? Is there an imaginary part?
Q2. Solve $ Ce^{x*jt} = 3j $ for C and x.
Q3. Solve $ Ce^{x*jt} = 5 $ for C and x.
Q4. True or False, 3j+6j*4j = -24 + 3j
Answers: Q1.) Real part = 1, Imaginary Part = 0
Q2.) C = 3, x = pi/2
Q3.) C = 5, x = 0
Q4.) True
