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Published byStewart Goodwin Modified over 6 years ago
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Complex Numbers Imaginary Numbers Vectors Complex Numbers
Add or Subtract Complex Numbers Multiplying Complex Numbers Dividing Complex Numbers
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Imaginary Numbers Key Point:
Imaginary numbers are numbers that result from taking the square root of negative numbers.
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Vectors Key Point: A vector is a line drawn from the origin to some given point. In electronics we call a vector a phasor. Graphically, the operator j rotates a phasor 90°.
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Complex Numbers Key Point:
Complex numbers are numbers that are part real and part imaginary. 4 + j3
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Add or Subtract Complex Numbers
Key Point: To add (or subtract) complex numbers, first add (or subtract) the real parts, then add (or subtract) the imaginary parts. (‑9+j6)+(12‑j2) =3+(j6‑j2) =3+j4
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Multiplying Complex Numbers
Key Point: Complex numbers are multiplied the same way we multiply algebraic terms. (2 + j3)(2 + j4) = 4 + j6 + j8 + j212 = 4 + j14 + (‑1)12 = ‑8 + j14
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Dividing Complex Numbers
Key Point: To divide complex numbers, multiply the numerator and denominator by the conjugate of the denominator. This will remove the imaginary part from the denominator.
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