# Math Help - complex number problem

1. ## complex number problem

Hello I need to get the argument of the complex number
z=2+3i
i get 56.3 degrees is this correct first of all ?

2. Originally Posted by wolfhound
Hello I need to get the argument of the complex number
z=2+3i
i get 56.3 degrees is this correct first of all ?
You are correct. In the complex plane you can use an Argand diagram with the horizontal axis being real and the vertical axis being imaginary

To find an answer in radians evaluate $\arctan \left(\frac{3}{2}\right)$ using the radians mode on your calculator

Wolfram says Wolfram's Answer which agrees with my calculator

3. If you can get the answer in degrees, why in the world can't you get it in radians? Either set your calculator to "radian" mode or multiply your answer, in degrees, by $\frac{\pi}{180}= \frac{3.1415926}{180}$ to change to radians.

4. Originally Posted by wolfhound
Hello I need to get the argument of the complex number
z=2+3i
i get 56.3 degrees is this correct first of all ?
Note that the argument of z is

$Arg(2+3i) = tan^{-1}3/2 = 56.3$

I'm sure there's a way to do this with special triangles, but I forget. Instead we will simply convert degrees to radians

Radians = (PI * Degrees ) / 180

$(56.3*pi)/180=.9826$

5. Thanks I can get 0.9826 ,
The thing thats worrying me is I have to write my answers in polar form in a test tomorrow and all the questions we have done in class, have fancy answers like 2Pi/3 in the polar form
so its ok to write r(cos0.9826 + isin0.9826) ?
thanks

6. Originally Posted by wolfhound
Thanks I can get 0.9826 ,
The thing thats worrying me is I have to write my answers in polar form in a test tomorrow and all the questions we have done in class, have fancy answers like 2Pi/3 in the polar form
so its ok to write r(cos0.9826 + isin0.9826) ?
thanks
Are you allowed calculators? If not then this becomes a problem. But I truly don't see a way of making 56 degrees into a nice number in radians.

So yes, that is correct.

If your teacher wants W as a polar representation then that is perfectly fine. Unless the question explicitly states "find a nice representation of this in radians" or something to that effect, what you have above is correct.

It's just not pretty :P

7. I see thanks ,one more question please , how do I write z=2i
in polar form?

8. Originally Posted by wolfhound
I see thanks ,one more question please , how do I write z=2i
in polar form?
Remember that the modulus is of the form

$z=a + bi$

In this case a = 0

So our argument is simply

$Arg(z) = \sqrt{2} = pi/4$

Then put that into polar. Pi/4 comes from special triangles.