# Complex numbers: negative absolute value (radius)?

I need to find a complex number that represented by the following poler representation:

($\mathbb r$, $\theta$) = ($-5$, $\pi \over 2$)

My question is: how is a negative radius (absolute value) possible?

What does it mean \ sign?

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It is not possible, at least not under the usual, standard definitions. Check this carefully. – DonAntonio Feb 5 at 15:37
I've seen things like this before; when I've encountered it, it has just meant to take the radius in the opposite direction. So, normally we would expect this to correspond to the point $5i$ in the complex plane (or $(0,5)$ if we identify it with $\Bbb R^2$. However, with the negative, it will correspond to $-5i$. I'm not going to say this is how it is for you, just when I've encountered it previously. – Clayton Feb 5 at 15:39
@Clayton The $\theta$ signs the angle with the positive X Axis, doesn't it? – user1798362 Feb 5 at 15:44
@user1798362: I'm not sure what you mean by signs the angle with the positive $x$-axis. The angle begins at $0^\circ$ there and rotates counterclockwise through an angle of $\pi/2$ in your case. – Clayton Feb 5 at 15:47
@Clayton Ok, thank you!! I have addition question and I'll better and it here instead of another ask: if $\theta$ = 45, than `a = b` in case $\mathbb z$ = `a + bi`? – user1798362 Feb 5 at 15:49
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## 1 Answer

$$z=r\cos\theta+ir\sin\theta$$

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