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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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graphical representation of a complex number
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
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
Find That Value, Absolutely
  • Try these
    • Graph the complex number
    • Find the absolute value
trig form of complex number
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 number6
Trig Form of Complex Number
  • Now we use and substitute into z = a + bi
  • Result is
  • Abbreviation is often
try it out
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
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
Quotient of Complex Numbers in Trig Form
  • Given
  • It can be shown that the quotient is
try it out10
Try It Out
  • Try the following operations using trig form
  • Convert answers to standard form
assignment
Assignment
  • Lesson 5.2
  • Page 349
  • Exercises 1 – 61 EOO