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Copyright © 2011 Pearson Education, Inc.
Trigonometric Formof Complex Numbers
Section 6.2
Complex Numbers, Polar Coordinates, and Parametric Equations
Copyright © 2011 Pearson Education, Inc. Slide 6-3
6.2
Figure 6.2
The Complex Plane
Copyright © 2011 Pearson Education, Inc. Slide 6-4
6.2
The absolute value or modulus of the complex number a + bi is defined by
.|| 22 babia
Definition: Absolute Valueor Modulus of a + bi
Copyright © 2011 Pearson Education, Inc. Slide 6-5
6.2
Figure 6.4
Trigonometric Formof a Complex Number
Copyright © 2011 Pearson Education, Inc. Slide 6-6
6.2
)sin(cos irz
If z = a + bi is a complex number, then the trigonometric form of z is
where and is an angle in standard position whose terminal side contains the point (a, b). An abbreviation for r(cos + i sin ) is r cis .
22 bar
Definition: Trigonometric Formof a Complex Number
Copyright © 2011 Pearson Education, Inc. Slide 6-7
6.2
If z1 = r1(cos 1 + i sin 1) and z2 = r2(cos 2 + i sin 2), then
z1z2 = r1r2 [cos (1 + 2) + i sin (1 + 2)]
and)].sin()[cos( 2121
2
1
2
1 irr
zz
Theorem: The Product andQuotient of Complex Numbers
Copyright © 2011 Pearson Education, Inc. Slide 6-8
6.2
The conjugate of the complex number r (cos + i sin ) is
)).sin()(cos( ir
Theorem: Complex Conjugates
