Imaginary Numbers Tyler Jang What Are Imaginary Numbers

Imaginary Numbers Tyler Jang

What Are Imaginary Numbers? Imaginary numbers are numbers that are not classified as real numbers. An imaginary number is a complex number that can be shown by multiplying a real number by i. I represents the square root of -1. All numbers whose square non-positive is an imaginary number.

Why Do We Have Them? Originally imaginary numbers were used to be able to solve equations with the square root of a negative number, making it possible do solve lots of equations that were not solvable before. Because it used to be that if you ended up with the square root of a negative number, that was as far as you could go, but now with “i” being the square root of -1, you don’t need to stop there, and you can keep going. https: //qph. ec. quoracdn. net/main-qimg-08572 ceea 8 ad 35422 a 6 ce 6 fe 0 c 298405? convert_to_webp=true

What Real Life Uses Do They Have? Although people call them imaginary, imaginary numbers do have many real life uses involving technology and software. One job that uses complex numbers frequently, is being an electrician. Complex numbers are used while finding how many amperes are in an electrical current. Musical displays also use imaginary numbers http: //classetice. fr/IMG/jpg/petit-4. jpg

How Do You Find the Square Roots Of Negative Numbers? For this question the best way to answer it is with an example. So if you want to find the square root of -4, it could help if you wrote it as the square root of 4(-1), then you can split it as the square root of 4 times the square root of -1, and we know the square root of -1 is I, so the answer would be 2 i.

How Do You Square a Complex Number? With the example 4 i, this time, ignore the “i”, and square the whole number, then multiply by -1. You can verify your answer by repeating the steps in the last slide.

What Is The Argand Diagram? The Argand Diagram is a diagram plotting complex numbers as points with the x-axis being the “real axis” and the y-axis being the “imaginary axis”. This diagram is important because is made the idea of imaginary numbers more acceptable. The points in this diagram can be shown as, z = x + iy, like you see in the picture. http: //i. stack. imgur. com/h. Wmu. Y. png

Is Zero An Imaginary Number? We know that the number zero is a real number, but can it be an imaginary number as well? In the Argand Diagram from the last slide, the real number axis and the imaginary number axis intersect at 0. This means that 0 must be a part of the imaginary number axis. Also in the first slide, we said that, all numbers whose square non-positive is an imaginary number. And 0^2 is equal to 0 which is not positive, it isn’t negative either, but it also isn’t positive so that would make zero an imaginary number. http: //1. bp. blogspot. com/-Z 65 V 1 tcugx 0/T 0 C 7 Ku. HAHw. I/AAAAAEY/m 2 nwc. KPqeg. A/s 1600/Screen+Shot+2012 -0219+at+09. 04. 06. png

Citations Rod, Pierce Imaginary Numbers: Mathis. Fun Apr 5 th 2014, accessed Oct 5 th 2016 https: //www. mathsisfun. com/numbers/imaginary-numbers. html Roberts, Donna Does Anyone Ever Really Use Complex Numbers: Regents. Prep 2012 accessed Oct 5 th 2016 http: //mathforum. org/library/drmath/view/53879. html Stapel, Elizabeth Complex Numbers: Introduction Purplemath 2014 Accessed Oct 5 th 2016 http: //www. purplemath. com/modules/complex. htm https: //en. wikipedia. org/wiki/Imaginary_number, November 22 nd 2016, Accessed Dec 1 st 2016, Wikipedia: Imaginary Number, http: //www. math. toronto. edu/mathnet/answers/imagexist. html, September 1 st 1997, Accessed Dec 1 st 2016, Spencer, Philip, University of Toronto: Answers and Explanations Weisstein, Eric W. "Argand Diagram. " From Math. World--A Wolfram Web Resource. http: //mathworld. wolfram. com/Argand. Diagram. html