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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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23.
Imaginary and Complex Numbers
23.1
Introduction to imaginary numbers
23.2
Complex numbers and complex planes
23.3
Adding and subtracting complex numbers
23.4
Complex conjugates
23.5
Multiplying and dividing complex numbers
23.6
Distance and midpoint of complex numbers
23.7
Angle and absolute value of complex numbers
23.8
Polar form of complex numbers
23.9
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.
We have over 1040 practice questions in AU Year 12 Maths for you to master.
Get Started NowPractice topics for Imaginary and Complex Numbers
23.1
Introduction to imaginary numbers
23.2
Complex numbers and complex planes
23.3
Adding and subtracting complex numbers
23.4
Complex conjugates
23.5
Multiplying and dividing complex numbers
23.6
Distance and midpoint of complex numbers
23.7
Angle and absolute value of complex numbers
23.8
Polar form of complex numbers
23.9
Operations on complex numbers in polar form