Complex Numbers

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Complex Numbers
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Definition of pure imaginary numbers
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Definition of pure imaginary numbers
i is not a variable it is a symbol for a
specific number
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Simplify each expression.
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Simplify each expression.
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Simplify.
To figure out where we are in the cycle divide
the exponent by 4 and look at the remainder.
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Simplify.
Divide the exponent by 4 and look at the
remainder.
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Simplify.
Divide the exponent by 4 and look at the
remainder.
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Simplify.
Divide the exponent by 4 and look at the
remainder.
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Definition of Complex Numbers
Any number in form abi, where a and b are real
numbers and i is imaginary unit.
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Definition of Equal Complex Numbers
Two complex numbers are equal if their real
parts are equal and their imaginary parts are
equal. If a bi c di, then a c and b d
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When adding or subtracting complex numbers,
combine like terms.
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Simplify.
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Simplify.
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Multiplying complex numbers.
To multiply complex numbers, you use the same
procedure as multiplying polynomials.
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Simplify.
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Simplify.
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The Habitat for humanity project utilizes
volunteers to help build house for low income
families who might not be able to afford the
purchase of a home. At a recent site, Habitat
workers built a small storage shed attached to
the house. The electrical blueprint for the shed
called for two AC circuits connected in series
with a total voltage of 220 volts. One of the
circuits must have an impedance of 7-10j ohms,
and the other needs to have an impedance of 95j
ohms. According to the building codes, the
impedance cannot exceed 20-5j ohms. Will the
circuits, as designed, meet the code?