Inconsistency of angle function in finding angle of vectors

Typing the command angle(1+i) yields an angle of 45 degrees, but typing angle(-1-2i) yields -2.0344. Why is the angle being measured clockwise from the x axis in one case and and counterclockwise in the other? Is there any more consistent way to find the angle of vectors, either measured clockwise or counterclockwise?

Answer 1

[the cyclist]

I would not characterize this as an inconsistency, so much as a convention to report the value in the range [-pi,pi], rather than the [0,2pi] that you expected. (I feel obligated to point out that this is quite explicit in the documentation.)

Regardless of your opinion on that, all you need to do is calculate the result modulus 2pi, to get what you want

mod(angle(1+i),2*pi)

ans = 0.7854

mod(angle(-2-i),2*pi)

ans = 3.6052

Answer 2

[Steven Lord]

Typing the command angle(1+i) yields an angle of 45 degrees,

No it doesn't. It returns the equivalent angle in radians, however.

A1 = angle(1+1i)

A1 = 0.7854

A2 = deg2rad(45)

A2 = 0.7854

abs(A2-A1)

ans = 0

but typing angle(-1-2i) yields -2.0344.

A3 = angle(-1-2i)

A3 = -2.0344

Correct.

Why is the angle being measured clockwise from the x axis in one case and and counterclockwise in the other?

From the documentation page for the angle function:

"theta = angle(z) returns the phase angle in the interval [-π,π] for each element of a complex array z. The angles in theta are such that z = abs(z).*exp(i*theta)."

If you want the angles to be in the interval [0, π] instead add the negative angle to 2*pi.

A3pos = 2*pi+A3

A3pos = 4.2487

theAngles = rad2deg([A3; A3pos])

theAngles = 2×1

-116.5651 243.4349

These angles are:

diff(theAngles)

ans = 360

360 degrees apart.