complex numbers polar form...remember complex numbers have two parts: a real part and an imaginary...
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![Page 1: Complex Numbers Polar Form...Remember complex numbers have two parts: a real part and an imaginary part (which includes i). Thus, the complex number, z, takes on the form Plotting](https://reader033.vdocuments.us/reader033/viewer/2022060510/5f26844836fac4518875c1f9/html5/thumbnails/1.jpg)
Complex Numbers Polar FormComplex Numbers
Real Numbers Imaginary Numbers
Rational Numbers Irrational Numbers
Integersnon‐integers(fractional)
Whole Numbers
Natural Numbers
negatives
0
(i)
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Remember complex numbers have two parts: a real part and an imaginary part (which includes i).
Thus, the complex number, z, takes on the form
z = a + bi
Examples: 3+7i, ‐2+5i, ‐7‐3i, etc.
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Plotting Complex Numbers
We use a cartesian coordinate plane to plot complex numbers.‐ The horizontal axis is our (Real) number line.‐ The vertical axis is the Imaginary number line.
A complex number is plotted as a combination of its two parts in much the same way as you would plot (x, y).
Thus, you can think of plotting a+bi as the same as plotting (a,b).
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Plot ethe following number on the complex plane:
A) 4+5i
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The Polar Form of a Complex Number
Z = 5 + 4i
![Page 6: Complex Numbers Polar Form...Remember complex numbers have two parts: a real part and an imaginary part (which includes i). Thus, the complex number, z, takes on the form Plotting](https://reader033.vdocuments.us/reader033/viewer/2022060510/5f26844836fac4518875c1f9/html5/thumbnails/6.jpg)
r is called the "modulus" of the complex number.
θ is called the "argument" of the complex number.
0≤θ<2π
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EX. Plot z = ‐1‐i√3 in the complex plane. Then write z in polar form.
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Ex2. Write z = 2cis60o in rectangular form.
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Multiplying "rCISθ"Remember how to multiply complex numbers?
Example
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Deriving the formula for multiplying "rCiSθ"Given andderive the formula for .
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Ex1. Given and
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Dividing "rCISθ"
Remember how to divide complex numbers?
Example
![Page 13: Complex Numbers Polar Form...Remember complex numbers have two parts: a real part and an imaginary part (which includes i). Thus, the complex number, z, takes on the form Plotting](https://reader033.vdocuments.us/reader033/viewer/2022060510/5f26844836fac4518875c1f9/html5/thumbnails/13.jpg)
Deriving the formula for dividing "rCiSθ"Given and
derive the formula for .
* Complete this verification on your own
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EX2. Given and
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ASSIGNMENTBlitzer
P. 696 #1‐52