what's the point of imaginary numbers?? (i ^2 equals -1) wow!!!?

Answer 1

Sure...
Let's say we have a number such that
i² = -1

Now can you think of a number satisfying that equation?
Now to solve, we get sqrt of both sides.
i = √(-1)

Now do you think a negative number has a square root? Nahh... That's why it is called imaginary numbers.

By using imaginary numbers, one can now get the square roots of any number, whether it be real or also imaginary. It also helps extend the number system into the universal set of numbers, complex numbers. i is an ultimate. Meaning you can write any number with it. You can write the square root of -1 with it. You can write the square root of i with it. You can write the square root of 3 + 7i with it. Meaning it can fill up all the remaining spaces of these roots.

^_^

Answer 2

here is another way to understand the mysterious number "i": normally, we think of numbers as lying on a line, so that multplying by a positive number is a "stretch": multiplying by 2, doubles the "length" (or distance from 0) of our original number, multiplying by 6 makes the length 6 times as long. so how to explain the mysterious fact that a negative number times a negative number is positive? well, we often say that multiplying by a negative number not only "stretches" our original length, but "flips" its direction. but, instead of a flip, i say you should regard it as a 180 degree rotation (or an "about face" as they say in the military). well, on a line, a "flip" is the same as a 180 degree turn, you still wind up back on the line where you started. but here is why thinking of it as a rotation is useful: what if, instead of going a half-turn, back on to your original line, you stopped halfway? that is, you only made a quarter-turn? that is what we mean by the imaginary number i: it is "1" rotated 90 degrees, so instead of being on the x-axis, at the 0 angle on a circle, its on the y-axis, or the 90 degree angle on a circle. well if you multiply by i again, you rotate 90 degrees more, which is 180 degrees, so now you are at -1. that is, i = i*1 i^2 = i*i = -1 so i^3 is just another 90 degree turn, and now we are on the bottom of the circle, at -i. finally, i^4 brings us full circle, back to 1 where we started. so if we want to know what i^k is, for any number k, we just divide by 4, and look at the remainder. if the remainder is 0, i^k = i^(4n + 0) = i^(4n) = (i^4)^n = 1^n = 1 if the remainder is 1, i^k = i^(4n + 1) = i^(4n)(i) = 1*i = i if the remainder is 2, i^k = i^(4n + 2) = i^(4n)(i^2) = 1(-1) = -1 if the remainder is 3, i^k = i^(4n + 3) = i^(4n)(i^3) = 1(i^3) = i^3 = i(i^2) = i(-1) = -i. thinking of i in this way, makes it clear what complex numbers are: they are just points in the plane, the "x part" is the real portion, and the "y-part" is the imaginary portion. and numbers that only have a "real part", that is, y = 0, all lie on the x-axis, which has the shape of a number line that we expect it to.

Answer 3

What would you say to someone who says
1+1=2 wow, what's the point?

There are lots of applications for complex numbers,
but I don't think you have enough mathematical
background to appreciate them. Just because you
don't understand something is no reason to mock it.

Answer 4

imaginary numbers (complex analysis) provides a solution for
x^2 = -1
this branch of mathematics is also used for analyzing complex circuits in electrical engineering

Answer 5

Aeronautics, rocket science, lots of things owe their power to the so-called "imaginary" numbers. (They're not really imaginary, they are complex.)

Answer 6

Since 4/5ths of todays students don't understand fractions....
lets just confuse the issue by saying, in electronics, that is refered to as "j".

Answer 7

there are problems tha are easier solved in the complex domain than in the real domain.

Answer 8

To make me drop out of college?