In Exercises 37–44, find the product of the complex numbers. Leave answers in polar form. z₁ = cos π/4 + i sin π/4 z₂ = cos π/3 + i sin π/3
Table of contents
- 0. Review of College Algebra4h 43m
- 1. Measuring Angles40m
- 2. Trigonometric Functions on Right Triangles2h 5m
- 3. Unit Circle1h 19m
- 4. Graphing Trigonometric Functions1h 19m
- 5. Inverse Trigonometric Functions and Basic Trigonometric Equations1h 41m
- 6. Trigonometric Identities and More Equations2h 34m
- 7. Non-Right Triangles1h 38m
- 8. Vectors2h 25m
- 9. Polar Equations2h 5m
- 10. Parametric Equations1h 6m
- 11. Graphing Complex Numbers1h 7m
- OLD 1. Angles and the Trigonometric Functions Coming soon
- OLD 2. Trigonometric Functions graphs, Inverse Trigonometric Functions Coming soon
- OLD 3. Trigonometric Identities and Equations Coming soon
- OLD 4. Laws of Sines, Cosines and Vectors Coming soon
- OLD 5. Complex Numbers, Polar Coordinates and Parametric Equations Coming soon
- NEW (not used) 7. Laws of Sines, Cosines and Vectors Coming soon
- NEW (not used) 8. Vectors Coming soon
- NEW(not used) 9. Polar equations Coming soon
- NEW (not used) 11. Graphing Complex Numbers Coming soon
0. Review of College Algebra
Complex Numbers
Multiple Choice
Identify the real and imaginary parts of each complex number.
3+2i3
A
a=3,b=23
B
a=3,b=2
C
a=23,b=3
D
a=3,b=3
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Verified step by step guidance1
Identify the standard form of a complex number, which is a + bi, where 'a' is the real part and 'b' is the imaginary part.
Examine the given complex number: 3 + 2i√3.
Determine the real part 'a' of the complex number, which is the coefficient of the real number without the imaginary unit 'i'. In this case, 'a' is 3.
Determine the imaginary part 'b' of the complex number, which is the coefficient of the imaginary unit 'i'. In this case, 'b' is 2√3.
Conclude that the real part is 3 and the imaginary part is 2√3, matching the format a = 3, b = 2√3.
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