Learn what complex numbers are, and about their real and imaginary parts.
Log in King Henclucky 8 years agoPosted 8 years ago. Direct link to King Henclucky's post “Wait, are _*all*_ numbers...” Wait, are all numbers complex? • (125 votes) J Cam 8 years agoPosted 8 years ago. Direct link to J Cam's post “No BUT --- ALL _REAL_ nu...” No BUT --- ALL REAL numbers ARE COMPLEX numbers. You need linear algebra or complex analysis to get the bigger picture, but for now, trust Stefan and me - real numbers are a special case for complex numbers just as a square is a special case for a rectangle. This is an argument over semantics ever since it was decided to call these multi-dimensional entities numbers. You might think of complex numbers as two-dimensional. If that isn't rough enough there are numbers with even more that two dimensions, as Stefan alluded to. Don't bother yourself with the ins and outs of multidimensional numbers until or unless there really is a need to. For now just learn the basics of complex numbers so you can get through the traditional undergrad stuff and have a basis for further learning should you decide to go there. (159 votes) 101Math a year agoPosted a year ago. Direct link to 101Math's post “I have 0 pet catsI have ...” I have 0 pet cats • (36 votes) rylan.wetsell a year agoPosted a year ago. Direct link to rylan.wetsell's post “Whenever someone ask how ...” Whenever someone ask how many cats you have, you can just say "It's complex" (64 votes) steenbergh 5 years agoPosted 5 years ago. Direct link to steenbergh's post “I have an issue with Prob...” I have an issue with Problem 2: • (25 votes) deepak 4 years agoPosted 4 years ago. Direct link to deepak's post “Hello there, steenbergh,...” Hello there, steenbergh, (57 votes) Anoushka B. 7 years agoPosted 7 years ago. Direct link to Anoushka B.'s post “If both real and imaginar...” If both real and imaginary parts of a complex number are 0, what kind of number is it? Or: is 0 real, complex or pure imaginary? • (21 votes) jwinder47 7 years agoPosted 7 years ago. Direct link to jwinder47's post “This is an interesting qu...” This is an interesting question. The real numbers are a subset of the complex numbers, so zero is by definition a complex number ( and a real number, of course; just as a fraction is a rational number and a real number). If we define a pure real number as a complex number whose imaginary component is 0i, then 0 is a pure real number. If we define a pure imaginary number as a complex number whose real component is 0 (or: where a=0 in the general component form for a complex number: a + bi), then 0 is also a pure imaginary number. This makes sense geometrically in the complex plane: the origin is the intersection of coordinate axes, so (0,0) is on both the real and the imaginary axes. (41 votes) JJ the Mad Scientist 8 years agoPosted 8 years ago. Direct link to JJ the Mad Scientist's post “I understand that imagina...” I understand that imaginary number can be helpful for solving math problems. However I am interested to know more on how it is used in quantum mechanics. • (10 votes) andrewp18 8 years agoPosted 8 years ago. Direct link to andrewp18's post “That is very difficult to...” That is very difficult to answer within the confines of the KA discussion page. If you really want to know, you can do a little searching on the net or you could read Hyperspace by Michio Kaku. (23 votes) Qing D Liang 5 years agoPosted 5 years ago. Direct link to Qing D Liang's post “Can you give the usage of...” Can you give the usage of imaginal number in reality? • (7 votes) VincentTheFrugal 5 years agoPosted 5 years ago. Direct link to VincentTheFrugal's post “They pop up in physics, a...” They pop up in physics, and you'll probably first see them when dealing with electromagnetism, or quantum mechanics. There's a good article about the usage of complex numbers here: https://galileospendulum.org/2012/06/09/imaginary-numbers-are-real/ If you think complex numbers are weird, wait until you find out about quaternions... which is useful for computer science. (10 votes) Eliza 4 years agoPosted 4 years ago. Direct link to Eliza's post “Some people have suggeste...” Some people have suggested that there are numbers that are NOT complex. Would anyone mind elaborating on what those are? • (4 votes) kubleeka 4 years agoPosted 4 years ago. Direct link to kubleeka's post “There are number systems ...” There are number systems beyond the complex numbers, but you don't see them in high-school math. This includes systems like the quaternions, which are 4-dimensional (like how the complex numbers are 2-dimensional), and the hyperreal numbers and surreal numbers, which include versions of infinite and infinitesimal numbers. (15 votes) akarnam999 6 years agoPosted 6 years ago. Direct link to akarnam999's post “I don't get the polynomia...” I don't get the polynomial equation showed above: (x*x) - 2x + 5 = 0 and how its complex number solution is 1 + 2i and 1 - 2i. • (7 votes) Kim Seidel 6 years agoPosted 6 years ago. Direct link to Kim Seidel's post “Use the quadratic formula...” Use the quadratic formula to solve the equation and the answers become x = 1+2i and x=1-2i. If you look at the other questions & answers already posted for this page, you will see one near the top of the list (currently the 2nd one) where the answer shows all the work for solving the equation using the quadratic formula. (8 votes) pathak.aojaswi a year agoPosted a year ago. Direct link to pathak.aojaswi's post “in the complex number sys...” in the complex number system, what is the value of the expression 16i^4- 8i^2 +4? (note: i = square root -1). i am very confused as to how to solve this problem. • (2 votes) KLaudano a year agoPosted a year ago. Direct link to KLaudano's post “16 * i^4 - 8 * i^2 + 4= ...” 16 * i^4 - 8 * i^2 + 4 (14 votes) Jimmy 8 years agoPosted 8 years ago. Direct link to Jimmy's post “Using the same logic that...” Using the same logic that all real numbers are complex, for example 52 = 52 + 0i, couldn't we say that all imaginary numbers are complex as well? For example 2i = 2i + 0, which would be a complex number, right? Thank you in advance • (5 votes) Enn 8 years agoPosted 8 years ago. Direct link to Enn's post “Yes, all imaginary number...” Yes, all imaginary numbers are also Complex Number as they can always be shown to have both a real and imaginary part. (7 votes)Want to join the conversation?
It just so happens that many complex numbers have 0 as their imaginary part. When 0 is the imaginary part then the number is a real number, and you might think of a real number as a 1-dimensional number.
The multidimensional number stuff is the kind of math that you really have to live in for awhile to understand and if you don't have a good motivation to understand then it can drive you crazy trying to get a quick understanding of what we are talking about. You need calc, trig, and analysis - you really do - to understand the reason why we teach complex numbers. Notice there aren't any complex number word problems in undergrad courses?
I have a real number of cats
I have an imaginary number of cats
I have a complex number of cats
ALL TRUE!What is the imaginary part of 21 - 14i?
The accepted answer was -14, where I'd expect it to be -14i, because the "imaginary part" is including the 'i', and the magnitude of the img part is -14...
Though the question refers to the "imaginary part of this complex number" it is really refering to the magnitude of the imaginary part. Think of a complex number as a position vector in the complex plane, since the direction of this "imaginary part" is specified (it is in the imaginary axis or the vertical axis in this case) we only need to give its magnitude in that direction as we already know its direction. When we say -14, we are merely saying "negative fourteen units in the imaginary axis/number plane". Hope that makes sense!
Hope this helps.
= 16 * (i^2)^2 - 8 * i^2 + 4
= 16 * (-1)^2 - 8 * (-1) + 4
= 16 * 1 - 8 * (-1) + 4
= 16 + 8 + 4
= 28
