PPT-Trigonometric Form of a Complex Number

Complex Numbers Recall that a complex number has a real component and an imaginary component z a bi Argand Diagram Real axis Imaginary axis z 3 2i z 3 2i a bi The absolute value of a complex number is its distance from the origin. Jami . Wang. . Period 3. Extra Credit PPT. Pythagorean Identities. sin. 2 . X + cos. 2 . X = 1. tan. 2. X + 1 = sec. 2. X. 1 + cot. 2. X = csc. 2. X. These . identities can be used to help find values of trigonometric functions. . A . ligand. is a species that can donate one or more lone pairs of electrons to form a coordinate bond with a central metal ion. . A central metal ion surrounded by ligands. . This is the . hexaquacopper. phys3330 – Spring 2012. Things you need to know about the complex number for this course: . 1.Perform algebraic operations on complex number and represent a given complex number graphically and express it in polar form.. Enea. Sacco. 2. Welcome to Calculus I!. Welcome to Calculus I. 3. Topics/Contents . Before Calculus. Functions. New functions from the old. Inverse Functions. Trigonometric Functions. Inverse Trigonometric Functions. Exponential and Logarithmic Functions. Jami . Wang. . Period 3. Extra Credit PPT. Pythagorean Identities. sin. 2 . X + cos. 2 . X = 1. tan. 2. X + 1 = sec. 2. X. 1 + cot. 2. X = csc. 2. X. These . identities can be used to help find values of trigonometric functions. . Section 8.4b. How do we evaluate this integral?. Trigonometric Substitutions. These trigonometric substitutions allow us to replace. b. inomials of the form. b. y single squared terms, and thereby transform a number. numbers. 1. Exponential Form:.  .  . Rectangular Form:. Real. Imag. x. y. f. r. =|z. |.  .  .  . The real and imaginary parts of a complex number in rectangular form are real numbers:. Real. Imag. Definitions. Conversions. Arithmetic. Hyperbolic Functions. Main page. Argand diagram. Im. . Re . If the complex number then . the . Modulus. of is written as and . the . Argument . The . imaginary . number . i. Simplifying square roots of negative numbers. Complex . Numbers, and their Form. The Arithmetic of Complex Numbers. Complex Conjugates. Division of Complex Numbers. Powers of . Sinusoids . and . Phasors. Read Alexander & . Sadiku. , Chapter 9 and Appendix B.. Homework . #11 . and Lab . #11 . due next week.. Quiz next week.. DC . Versus AC. In a direct-current (DC) circuit, current flows . How can you evaluate trigonometric functions of any angle?. What must always be true about the value of r?. Can a reference angle ever have a negative measure?. General Definitions of Trigonometric Functions. 1.. 2.. 3.. 4.. 5.. f. (. x. ) = . x. 2. . – 18. x. + 16. f. (. x. ) = . x. 2. . + 8. x. – 24. Find the zeros of each function.. Define and use imaginary and complex numbers.. Solve quadratic equations with complex roots.. 1. Exponential Form:.  .  . Rectangular Form:. Real. Imag. x. y. f. r. =|z. |.  .  .  . The real and imaginary parts of a complex number in rectangular form are real numbers:. Real. Imag. x. =. Re(z). Outline. Linear Systems Theory. Complex Numbers. Polyphase. Generators and Motors. Phasor. Notation. Reading - Shen and Kong - Ch. 1 . True / False. 1. In Lab 1 you built a motor about 5 cm in diameter. If this motor spins at 30 Hz, it is operating in the quasi-static regime..