In Exercises 11–14, plot each complex number. Then write the complex number in polar form. You may express the argument in degrees or radians. 1 − i
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
11. Graphing Complex Numbers
Polar Form of Complex Numbers
Multiple Choice
Express the complex number in polar form.
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Verified step by step guidance1
Identify the real part (a) and the imaginary part (b) of the complex number z = 7 + 11i. Here, a = 7 and b = 11.
Calculate the magnitude (modulus) of the complex number using the formula: |z| = \(\sqrt{a^2 + b^2}\). Substitute a = 7 and b = 11 into the formula.
Determine the argument (angle θ) of the complex number using the formula: θ = \(\tan\)^{-1}(b/a). Substitute a = 7 and b = 11 into the formula to find θ in degrees.
Express the complex number in polar form using the formula: z = |z|(\(\cos\) θ + i\(\sin\) θ). Use the magnitude and argument calculated in the previous steps.
Verify the polar form by checking if the calculated magnitude and angle match the given polar form expression.
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