Imaginary & Complex Numbers EQ : Why do imaginary numbers exists and how do you...
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Transcript of Imaginary & Complex Numbers EQ : Why do imaginary numbers exists and how do you...
Imaginary & Complex Numbers
EQ: Why do imaginary numbers exists and how do you add/subtract/multiply/divide imaginary numbers?
Why do we need imaginary numbers? Allow us to make calculations that
otherwise would not be possible (ex. Electric circuits)
i2=
Powers of i i1 i2 i3 i4 i5 i6 i7 i7 ...
Simplified form
i -1 -i 1 i -1 -i 1 ...
How to re-write radicals using “i”
Re-write as multiple of -1
Separate radicals
Substitute
Ex 1) Re-write using the number “i”
Ex 2) Simplify
Change to “i” form first!!!
Multiply
Substitute i2 = -1
Factor
Multiply coefficients
You Try! – Simplify each imaginary expression
a.
b.
c.
COMPLEX NUMBERS
Real #sEx) 2, -5,
1.3
Imaginary #s
Ex) 5i
RationalIrrationalIntegers etc. a+bi
Ex 3) Simplify )31()46( ii
Ex 4)
Ex 5)
Conjugate
The opposite operation between two terms.
Ex) 5 + 2i conjugate: 5 – 2i
Imaginary numbers may never be in the denominator
To eliminate them, multiply the numerator & the denominator by the conjugate
Ex 6) Simplify by rationalizing the denominator
Multiply top & bottom by conjugate
Substitute i2 = -1
Ex 7) Simplify by rationalizing the denominator
Calculator: To use the imaginary number press
2nd ,
Exit Ticket: Use the calculator to simplify:
1.
2.
)31()46( ii
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