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Trigonometric Form of Complex Numbers - PowerPoint PPT Presentation
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Trigonometric Form of Complex Numbers. Lesson 5.2. Graphical Representation of a Complex Number. Graph in coordinate plane Called the complex plane Horizontal axis is the real axis Vertical axis is the imaginary axis. 3 + 4 i •. -2 + 3 i •. • -5 i. Absolute Value of a Complex Number.
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Trigonometric Form of Complex Numbers
Lesson 5.2
Graphical Representation of a Complex Number
- Graph in coordinate plane
- Called the complex plane
- Horizontal axisis the real axis
- Vertical axis is the imaginaryaxis
3 + 4i•
-2 + 3i•
• -5i
Absolute Value of a Complex Number
- Defined as the length of the line segment
- From the origin
- To the point
- Calculated byusing PythagoreanTheorem
3 + 4i•
Find That Value, Absolutely
- Try these
- Graph the complex number
- Find the absolute value
Trig Form of Complex Number
- Consider the graphical representation
- We note that a righttriangle is formed
a + bi•
r
b
θ
a
How do we determine θ?
Trig Form of Complex Number
- Now we use and substitute into z = a + bi
- Result is
- Abbreviation is often
Try It Out
- Given the complex number -5 + 6i
- Write in trigonometric form
- r = ?
- θ = ?
- Given z = 3 cis 315°
- Write in standanrd form
- r = ?
- a = ?
- b = ?
Product of Complex Numbers in Trig Form
- Given
- It can be shown that the product is
- Multiply the absolute values
- Add the θ's
Quotient of Complex Numbers in Trig Form
- Given
- It can be shown that the quotient is
Try It Out
- Try the following operations using trig form
- Convert answers to standard form
Assignment
- Lesson 5.2
- Page 349
- Exercises 1 – 61 EOO
