Question

how do i find the slope of this complex number 2401i?

Answer 1

id say by plotting it, but i dont recall ever hearing about the slope of a complex number before

Answer 2

if anything its the tangent of b/a

Answer 3

slope??

Answer 4

would taht result in a 0 slope?

Answer 5

no, the slope of a vertical line is simply undefined

Answer 6

not slope
i mean degrees

Answer 7

you are on the imaginary axis. there is no slope, and in any case a complex number is a point in the complex plain, not a line, so it has not slope

Answer 8

your on the postive i axis if anything ....

Answer 9

like that

Answer 10

so how would i apply the DeMoivre's theorem is i need the cube root of this imaginary number?

Answer 11

wouldnt you just fill in the parts that it requires?

Answer 12

2401i= 0+2401i there fore according to DeMoivre's theorem 2401^1/4(cos0+i sin0)

Answer 13

but that says its not correct

Answer 14

i think the 0 is in the wrong spot

Answer 15

hmm you mean as a part of the standard form of the imaginary number 0+2401i?

Answer 16

z^n= r^n (cos nθ + i sin nθ)

right?

Answer 17

correct for the trigonometric form of a complex number

Answer 18

\[z^{1/3}=2401^{1/3}(cos(\frac{pi}{6})+isin(\frac{pi}{6}))\]
if im reading this right

Answer 19

thanks for your patience. the question reads what are the fourth roots of 2401i.

Answer 20

oh, cause i read "so how would i apply the DeMoivre's theorem is i need the cube root of this imaginary number?" :)

Answer 21

oh who knew?
\[7^4=2401\]!!

Answer 22

so I need the 4 root of the complex number
which needs to be in trig form but i cannot figure out theta

Answer 23

theta = pi/2

Answer 24

why is it pi/2?

Answer 25

@amistre i wolframed it. had no idea that it is \(7^4\)

Answer 26

plot 2401i in the complex plane; youll see that its sitting right there n the "y" axis

Answer 27

lol, that one of the most common 4ths too aint it?

Answer 28

ok so x is zero and it only goes up the imaginary axis hence pi/2

Answer 29

guess that was the clue that it was 4th roots they were after

Answer 30

i havent even taken my finals yet and ive got 5 As regardless ..... the 6th one is prolly an A, if not its a B+

Answer 31

any dancing this semester?

Answer 32

yes! that is the graph, how did you get those angles?

Answer 33

not this semester ...

Answer 34

divided \(\frac{\pi}{2}\) in by 4, got \(\frac{\pi}{8}\) and then divided the cirlce up into 4 equal parts

taking all math or something more fun?

Answer 35

3 maths, religion, science, and computers

Answer 36

one of these things is not like the others....

Answer 37

ok thanks a lot for your help guys

Answer 38

yw

Answer 39

\[7\left(\cos(\frac{\pi}{8})+i\sin(\frac{\pi}{8})\right)\] etc

Answer 40

awesome thanks