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Operations on complex numbers in polar form
- Lesson: 1a8:30
- Lesson: 1b2:17
- Lesson: 1c3:36
- Lesson: 2a8:08
- Lesson: 2b2:44
- Lesson: 2c2:05
- Lesson: 36:52
Operations on complex numbers in polar form
Let's find out how to perform some basic operations on complex numbers in polar form! We will briefly introduce the notion of the exponential form of a complex number, then we will focus on multiplication and division on complex numbers in polar form.
Related concepts: Imaginary zeros of polynomials,
Lessons
Note:
Polar form real parta=∣z∣cosθ
imaginary partb=∣z∣sinθ
z=∣z∣(cosθ+isinθ)
When …
Multiplying: multiply the absolute values, and add the angles
Dividing: divide the absolute values, and subtract the angles
Exponential formz=∣z∣eiθ
Polar form real parta=∣z∣cosθ
imaginary partb=∣z∣sinθ
z=∣z∣(cosθ+isinθ)
When …
Multiplying: multiply the absolute values, and add the angles
Dividing: divide the absolute values, and subtract the angles
Exponential formz=∣z∣eiθ
- 1.Multiplying complex numbers in polar forma)4(cos(35π)+isin(35π))⋅8(cos(32π)+isin(32π))b)(cos(170∘)+isin(170∘))⋅5(cos(45∘)+isin(45∘))c)3(cos(π)+isin(π))⋅(cos(5π)+isin(5π))⋅6(cos(32π)+isin(32π))
- 2.Dividing complex numbers in polar forma)20(cos(25π)+isin(25π))÷6(cos(32π)+isin(32π))b)3(cos(43π)+isin(43π))÷12(cos(6π)+isin(6π))c)(cos(262∘)+isin(262∘))÷(cos(56∘)+isin(56∘))
- 3.Convert the following complex number to exponential form
z=3+i
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9.
Imaginary and Complex Numbers
9.1
Introduction to imaginary numbers
9.2
Complex numbers and complex planes
9.3
Adding and subtracting complex numbers
9.4
Complex conjugates
9.5
Multiplying and dividing complex numbers
9.6
Distance and midpoint of complex numbers
9.7
Angle and absolute value of complex numbers
9.8
Polar form of complex numbers
9.9
Operations on complex numbers in polar form
Don't just watch, practice makes perfect.
Operations on complex numbers in polar form
Don't just watch, practice makes perfect.
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Get Started NowPractice topics for Imaginary and Complex Numbers
9.1
Introduction to imaginary numbers
9.2
Complex numbers and complex planes
9.3
Adding and subtracting complex numbers
9.4
Complex conjugates
9.5
Multiplying and dividing complex numbers
9.6
Distance and midpoint of complex numbers
9.7
Angle and absolute value of complex numbers
9.8
Polar form of complex numbers
9.9
Operations on complex numbers in polar form