MAC1105 Lecture 3: 1.3 Complex Numbers; Quadratic Equations-Complex Number System Notes

23 views4 pages

plummoose320

25 Feb 2017

School

Miami Dade College

Department

Mathematics: Calculus & Pre-Calculus

Course

MAC1105

Professor

Montañez

For unlimited access to Class Notes, a Class+ subscription is required.

Document Summary

Provide a generalization to the terms listed in this section. While noted as i, is the given number whose square is going to be 1, which notes that: Numbers that occur in the form of a ratio. Numbers that would not occur in the form of a ratio. This is a type of number system that comes from introducing i, which is the imaginary number. Any numbers that are in the form of where the following occur: a and b are real numbers, z is the standard form. B is the imaginary part z = a + bi. Complex numbers examples i2 = i i = 1: 2+3i. Imaginary part: -6: -3+(-4)i = 3-4i. Imaginary part: -4: -(5)-(-2)i = -5+2i. Speci c complex numbers examples: a+0i = a. In this case, this help note that the real numbers are just subsets of the complex numbers: 0+bi = bi.

Related Questions

I posted the chart and questions. I will still write them if they are not clear.

A company manufactures high powered fountains that can be used to create elaborate water shows set to light and music. The company makes three models of fountains, each of which can launch a vertical stream of water to a different height, as incdicated in the table above ( see picture).

Complete the following tasks, filling in the misssing values in the table back to its starting level.

32) Find the time water would take to fall from each height in the table back to its starting level. Round your answer to the nearest thousandth of a second.

33) Find the initial upward velocity required for Fountain B to launch the water to its maxiumum height. Round your answer to the nearest tenth of a foot per second.

34) Create a function that will give you the minimum initial upward velocity, v , required to launch water to any given height, h.

You can see the image here too: http://imgur.com/a/n0n9D

Also there is another question i am stuck on: Here it is

Consider the properties of complex numbers.

9) Which of the following is true about the complex number a + bi

A) a and b are both real

B) a is real and b is imaginary

C) a is imaginary and b is real

D) a and b are both imaginary

E) all of the above

My text book says a complex number written in standard form is a number a + bi where a and b are real numbers. The number a is the real part of the complex number, and the number bi is the imaginary part.

So i know that A is correct but i am confused for option B, because isn't bi the imaginary part?

Thanks for whoever helps, it means alot.

ey table is seen below xeecions tor Chapter 1 12, Fori, b â¬ Î.el * b-aa (0 (D 14 ForVEQ r the operation defined in Example 1 on the wr John Sue Henry. P iDFor 15ine if is ass ociative by determining if the final six engu defined ang property (ii)of Theorem 1 . So no element i if the operntion debined in Example 1 of Emle if each element has an inverse Section 1.3 Groups iw comutatityn ild Chapter 3 where the Funda the exercises that follow etermining why they are not Write out the Cayley table for the gru(o)nud lensify thee element the 10 elements of the group Z 18 its operation uses ts in the first coordinnte and +2 in the secotu Ldessity the Zn and write out the Cayley table. Reeall th of each element does Theorem 1.14 tell us aont the entries in the Cayley table ol s xrewp that is set with exactly one element. A {n), will always form group since there 19. What nly one way to define an operation on the set. Be sure to shhow that the properi combination of the usual notice what set the rule is be of a group all hold. 21. We can create even create groupe with games! Consider four cups placed in a ssare patter table. If we have a penny in one of the cups there are four ways we can move it to t cup: Horizontally, Vertically, Diagonally, or Stay nehere it is. We will p, S. To define nn operation, consider two movements in a row, v.e.,m ove the penny as r tells us to, then after that move the penny as y instruets. the set of integers the set of real numbers n the set of positive integers. e set of positive integers. n the set of positive integers. on the set of integers e set of negative integers. we ple, HV D since if we first move it horizontally and then vertically nltogether e moved it diagonally. Create the Cayley table for this group, identify the identity and the inverse of cach element 22. Prove that the set A 0 under matrix multiplication. Is it abelian? 23. Verify that 3(R) is a group using the addition of funetions as defined in Example 13 e set of nonzero rational n he set of nonzero real num n on the set R (-1 Section 1.4 Basic Algebra in Groups 24. Prove the Cancellation Law (Theorem 1.20). Do not use any theorems that occur after it in the text ssociative, commutative, has roof or counterexample fo 25. Assume G is a group and a e G. Consider a fixed integer k and use PMI (Theorem 0.3) to prove that for all nEN, a aYou will need to consider cases here since k can be positive, negative, or o 26. Prove Theorem 1.23 (ii) for the case of n > 0 and m

MAC1105 Lecture 3: 1.3 Complex Numbers; Quadratic Equations-Complex Number System Notes

Document Summary

Get access

Related Documents

MAC1105 Lecture 1: 1.3 Complex Numbers; Quadratic Equations in the Complex Number System Notes

MAC1105 Lecture 3: 1.4 Complex Numbers; Quadratic Equations in the Complex Number System Notes

MAC1105 Study Guide - Quiz Guide: Unit Circle, Quadratic Formula, Quadratic Equation

Related Questions