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Definition Multiplication Arguments Roots
Complex Numbers in Exponential Form
Bernd Schr¨
oder
Bernd Schr¨
oder Louisiana TechUniversity, College of Engineering and Science
Complex Numbers in Exponential Form
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Complex Numbers in Exponential Form: Multiplication and Roots, Exercises of Calculus
Definitions, formulas, and examples for complex number multiplication in exponential form and finding the nth roots of a complex number. It covers the concepts of arguments, roots, and visualization of quotients and powers.
What you will learn
- How do you multiply complex numbers in exponential form?
- What is the relationship between complex number multiplication and roots?
- How do you visualize complex number quotients and powers?
- What are the arguments in complex number multiplication?
- How do you find the roots of a complex number?
Typology: Exercises
2021/2022
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Complex Numbers in Exponential Form
Bernd Schr¨oder
Bernd Schr¨oder Louisiana Tech University, College of Engineering and Science
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Introduction
Bernd Schr¨oder Louisiana Tech University, College of Engineering and Science
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ℜ(z)
ℑ(z)
Bernd Schr¨oder Louisiana Tech University, College of Engineering and Science
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ℜ(z)
ℑ(z)
Bernd Schr¨oder Louisiana Tech University, College of Engineering and Science
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ℜ(z)
ℑ(z)
x
y
Bernd Schr¨oder Louisiana Tech University, College of Engineering and Science
logo
ℜ(z)
ℑ(z)
x
y
O
Bernd Schr¨oder Louisiana Tech University, College of Engineering and Science
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ℜ(z)
ℑ(z)
x
y
θ O
Bernd Schr¨oder Louisiana Tech University, College of Engineering and Science
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ℜ(z)
ℑ(z)
x
y
θ O
r =
x^2 + y^2
Bernd Schr¨oder Louisiana Tech University, College of Engineering and Science
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ℜ(z)
ℑ(z)
x
y
θ O
r =
x^2 + y^2
y = r sin(θ )
Bernd Schr¨oder Louisiana Tech University, College of Engineering and Science
logo
ℜ(z)
ℑ(z)
x
y
θ O
r =
x^2 + y^2
y = r sin(θ )
x
Bernd Schr¨oder Louisiana Tech University, College of Engineering and Science
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ℜ(z)
ℑ(z)
x
y
θ O
r =
x^2 + y^2
y = r sin(θ )
x = r cos(θ )
z = x + iy
Bernd Schr¨oder Louisiana Tech University, College of Engineering and Science
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ℜ(z)
ℑ(z)
x
y
θ O
r =
x^2 + y^2
y = r sin(θ )
x = r cos(θ )
z = x + iy = r(cos(θ ) + i sin(θ ))
Bernd Schr¨oder Louisiana Tech University, College of Engineering and Science
logo
ℜ(z)
ℑ(z)
x
y
θ O
r =
x^2 + y^2
y = r sin(θ )
x = r cos(θ )
z = x + iy = r(cos(θ ) + i sin(θ ))
The connection is
x + iy = r cos(θ )
Bernd Schr¨oder Louisiana Tech University, College of Engineering and Science
logo
ℜ(z)
ℑ(z)
x
y
θ O
r =
x^2 + y^2
y = r sin(θ )
x = r cos(θ )
z = x + iy = r(cos(θ ) + i sin(θ ))
The connection is
x + iy = r cos(θ ) + ir sin(θ )
Bernd Schr¨oder Louisiana Tech University, College of Engineering and Science