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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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19.
Imaginary and Complex Numbers
19.1
Introduction to imaginary numbers
19.2
Complex numbers and complex planes
19.3
Adding and subtracting complex numbers
19.4
Complex conjugates
19.5
Multiplying and dividing complex numbers
19.6
Distance and midpoint of complex numbers
19.7
Angle and absolute value of complex numbers
19.8
Polar form of complex numbers
19.9
Operations on complex numbers in polar form
Don't just watch, practice makes perfect
Practice topics for Imaginary and Complex Numbers
19.1
Introduction to imaginary numbers
19.2
Complex numbers and complex planes
19.3
Adding and subtracting complex numbers
19.4
Complex conjugates
19.5
Multiplying and dividing complex numbers
19.6
Distance and midpoint of complex numbers
19.7
Angle and absolute value of complex numbers
19.8
Polar form of complex numbers
19.9
Operations on complex numbers in polar form