Can someone give me a quick run down on imaginary numbers?

[zylander]

I have a trig test tomorrow that I have been studying for. Our teacher has her tests from last semester saved online for us to study and practice with and before a test she tells us which problems on the old test to look at to study. One of the problems she gave us to look at involves imaginary numbers (we havent done anything with imaginary numbers in class), I HATE imaginary numbers and its the one thing I never really understood from algebra. Ive got pretty much everything else for the test down except this, could someone give me a quick lecture on imaginary numbers, or help me solve the following problem? All I remember is that i= -1.

Here is the problem;

a. Express 2(cos(tan^-1(4)+isin(tan^-1(4)) in the form a+bi where a and b are real numbers.


b. Express -3^(1/2)-i (negative root 3 minus i)
for this one, negative root 3 could be tan of 2pi/3, but what is -i?

 

[mugs]

i != -1

i == sqrt(-1)

 

[zylander]

oh yeah, i^2 = -1. oops.

 

[amicold]

This trig stuff is way over my head, I could never grasp it. The numbers aren't real, so fvck em.

 

[Alone]

0.999... = 1

 

[Alone]

Originally posted by: amicold
This trig stuff is way over my head, I could never grasp it. The numbers aren't real, so fvck em.

I'll never use this kind of math in real life. That's probably why I'll work for pennies my entire life.

 

[tasmanian]

Originally posted by: Alone
......_
0.999 = 1

Fixed. Ignore the .

 

[AgaBoogaBoo]

Originally posted by: mugs
i != -1

i == sqrt(-1)

Spoken like a true programmer 😀

 

[potoba]

look at euler formula. That's the only thing you need to know to do the above problems

Edit: you dont even need the euler's formula to solve these problem. Just use the most simple definition of complex numbers. Ex, the firtst question, you only need to take arctan(4) to get the real numbers a,b

 

[Fourier Transform]

Complex numbers aren't too bad.

You can think of complex numbers graphically on an X-Y plane, except the X axis is now known as the Real axis and the Y axis is the Imaginary axis.

So, for example, the number 3 + 4i would represent a point with the coordinates (3,4).

Now, if you look at this point, it is a certain distance away from the origin (the magnitude) and it makes a certain angle with the positive real axis (phase or argument).

The mag. of a complex number z = a + bi is denoted by |z| and is found using the pythagorean theorem. I.e. |z| = sqrt (a^2 + b^2). The argument is denoted as arg(z) or <z and is given by arctan(b/a). Draw it out on paper and it'll make more sense to you.

z = a + bi is said to be in rectangular form and z = |z|exp(i*arg(z)) is said to be in polar form.

As far as your questions go:

1) Straight forward. Multiply the 2 in the bracket to get 2 cos (...) + i*2sin (...)

2) I assume they want it converted to polar form? In that case, follow what I described above.

 

[cubby1223]

Nobody likes imaginary numbers like eleventeen.