Question

How do I convert complex numbers into trigonomic functions?

5(cos 53.13* + i sin 53.13*) = 5 cis 53.13*

Answer 1

complex numbers are not trig functions

Answer 2

if you want to turn your "trig form" into standard form \(a+bi\) then you need only evaluate
you will need a calculator for this one

Answer 3

looks like you have \(3+4i\) here

Answer 4

how do i imput the cis into my calculator?

Answer 5

you don't

Answer 6

you use \(\cos(53.13)\) and \(\sin(53.13)\)

Answer 7

I don't?

Answer 8

ohh, ok

Answer 9

cis is a notational shortcut

Answer 10

and evaluate everything before the equal?

Answer 11

http://www.wolframalpha.com/input/?i=5%28cos+%2853.13%29+%2B+i+sin+%2853.13%29%29

Answer 12

the expression you see on the right is just notational shorthand for the expression on the left

Answer 13

ohh, ok i get it!

Answer 14

it stands for "cosine theta plus i sine theta" "cis"

Answer 15

from that link, is the radius or the angle the trigonomic function?

Answer 16

5 is the radius, 53.13 is the angle but you knew that already since you had
\[5\left(\cos(53.13)+i\sin(53.13)\right)\]

Answer 17

right

Answer 18

what you get out of this is the part that says
"result 3.0001 +3.999 i" which probably means this is supposed to be \(3+4i\) in standard form

Answer 19

the reason it is not exact is that 53.13 is not exact

Answer 20

is the trigonomic function "-4.8093+1.36772*i" ?

Answer 21

ok hold on for a second, i sense some serious confusion
"-4.8093+1.36772*i" is not a trigonometric function at all. it is a complex number

Answer 22

\(\sin(x), \cos(x), \tan(x)\) are trig functions
\(a+bi\) or \(r\left(\cos(\theta)+i\sin(\theta)\right)\) are numbers

Answer 23

and so
\[5\left(\cos(53.13)+i\sin(53.13)\right)\] is just a number. it is a complex number, but it is a number

Answer 24

how do i change it to trigonomic form?

Answer 25

and in fact, it is the number \(3+4i\)

Answer 26

\[5\left(\cos(53.13)+i\sin(53.13)\right)\] is already in trig form.

Answer 27

huh
so the question is the answer?

Answer 28

\(r(\cos(\theta)+i\sin(\theta))\) is trig form
\(a+bi\) is standard form

Answer 29

so that means that the equation i posted first is the trigonomic form of that equation?

Answer 30

i cannot imagine the question was "express \(5\left(\cos(53.13)+i\sin(53.13)\right)\) in trig form" as it is already in trig form
but i could be wrong
the question might be "express \(3+4i\)in trig form"
or
"express \(5\left(\cos(53.13)+i\sin(53.13)\right)\) in standard form"

Answer 31

yes, it is already in trig form.

Answer 32

the question was to change the complex number in a previous question to trig form, and the answer to the other question was in trig form already

Answer 33

so i guess.........its the answer for this question too

Answer 34

what was the exact question?

Answer 35

"Use your graphing calculator to convert he complex number to trigonomic form in the problems below:

then it said the question was #47

#47 is: Write each complex number in trogonomic form. Round all angles to the hundreth os a degree" 3 + 4i

Answer 36

aaaah so that was the question, wrote \(3+4i\) in trig form, and the answer was \(5\left(\cos(53.13)+i\sin(53.13)\right)\) good enough

Answer 37

yes, that is the answer for sure

Answer 38

and then that was also the answer for 55

Answer 39

lol, two answers for the price of one

Answer 40

so maybe the question is, how do you write \(3+4i\) in trig form?

Answer 41

do you know how to do that?

Answer 42

umm, actually, no

Answer 43

well that is what you need to turn \(3+4i\) in to \(5\left(\cos(53.13)+i\sin(53.13)\right)\)

Answer 44

so, in the end, the final answer is 5(cos(53.13)+isin(53.13)) ?

Answer 45

you need two numbers, \(r\) and \(\theta\) to turn \(a+bi\) in to \(r\left(\cos(\theta)+i\sin(\theta)\right)\)

Answer 46

yes that is the answer, but i sense that it is not clear how to get there

Answer 47

r = 5, and theta = 53.13

Answer 48

yea i know, but do you know where these numbers come from?

Answer 49

yes

Answer 50

r = square root of : 3^2 + 4^2 = square root of 25

Answer 51

ok then you are done

Answer 52

ok, thanks for helping me out! I was totally confused!