Question #af849

2 Answers
Bill K.
Jul 21, 2015

arctan(7/3)-pi\approx -1.976\mbox{ radians}\approx -113.2^{\circ}

Explanation:

First, mark the point -(3+7i)=-3-7i in the complex plane. Note that it is in the 3rd quadrant. This means that its argument, or angle (typically taken to be between -pi and pi) is arctan((-7)/(-3))-pi=arctan(7/3)-pi\approx -1.976\mbox{ radians}\approx -113.2^{\circ}.

You need to subtract pi from arctan(y/x) in this case because of the fact that the point is in the 3rd quadrant. The arctangent function gives an output between -pi/2 and pi/2 radians.

bp
Jul 22, 2015

The answer already given is perfectly alright.

Explanation:

Just to make it more clear, it can be stated that argument is measured in anticlockwise direction from positive x axis and it is positive till it is less than 180 degrees. In this case the angle that vector -3-7i makes with x axis is in the third quadrant, hence more than 180 degrees. In this case the angle is measured in clockwise direction , hence it is -1.976 radians.

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