Question

A complex number will, in general, have _____ fifth complex roots.
Help fill in the blank? :o

Answer 1

Whatever the number complex root, that's how many there are. 5 5th complex, 4 4th complex, 3 3rd complex, etc.

Answer 2

Oh okay that's easy! :)

Answer 3

how do you find the fourth root of \[-1+i \sqrt{3}\] ?

Answer 4

I'm not positive, but I think we need it in polar form first. At least I know how to do it from polar form, lol.

Answer 5

You remember how to put it in polar form? xD

Answer 6

NO D: >.< :(

Answer 7

Forgot since last night xD Bleh. Well, we need r(costheta + isintheta). r comes from the same old pythagorean theorem thing.
\[r = \sqrt{a ^{2}+b ^{2}}\]. A is your negative 1 and b is your sqrt(3) So we can start off by getting r :3

Answer 8

So it'd be 1+ 3 = 4 ?

Answer 9

Square root of 3 Squared is 3 ?

Answer 10

Right. So you would just have sqrt of 4 which is 2 xD

Answer 11

So r = 2 :P
Now to get the angle, we need to say that
\[\tan \theta = \frac{ b }{ a }\]

Answer 12

so, \[4\sqrt{2}\].. b is \[i \sqrt{3} ?\]

Answer 13

Whoa, wait xD Not sure where 4rt2 came from o.o

a = -1
b = \[\sqrt{3}\] no i included
\[r = \sqrt{(-1)^{2}+\sqrt{3}^{2}} = \sqrt{4} = 2\]
This is where we are so far xD Now since a = -1 and b = sqrt 3, we need to say:
\[\tan \theta =\frac{ \sqrt{3} }{ -1 }\]

Answer 14

ohh, okkay !, which is \[-\sqrt{3} ??\] D:

Answer 15

Lol, yes xD No need to freak out, that one is correct :P So now, tangent is negative in the 2nd and 4th quadrants. So if our original rectangular says
\[-1 + i \sqrt{3}\], then which quadrant is that,2 or 4?

Answer 16

2 ?

Answer 17

Yep :p The rectangular form basically says left one and up rt(3) xD So now, in the 2nd quadrant, any idea where tan(theta) = -sqrt(3)?

Answer 18

1 quadrant ?

Answer 19

._o

Answer 20

No, no, no, it's in the 2nd quadrant xD That's what I was just basically asking :P



Because tangent is the division of y/x, the only way it can be negative is if it's in a quadrant where either x or y, but not both, are negative. So on that circel, you can see that quadrant 2 and quadrant 4 are the places where you ciuld have a negative tangent.

Answer 21

If you're still alive xD