1-3 powers of i, operations with 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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Do you see the pattern?
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Do you see the pattern now? It repeats after 4.
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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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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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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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Equality of Complex numbers

• If a bi c di, then a c and bi di.