# I am confuse in finding Argumnet of Complex Number

• urduworld
In summary: For polar form, you can use the same logic. If your angle is in the 2nd or 3rd quadrant, you have to add 180 degrees to the value given by the inverse tangent function. In the 3rd quadrant, you have to add 360 degrees, but 180 will work just as well. You should be able to work out the details for yourself.
urduworld
hi PF

consider (2+1i) then Tan^-1(2/2) which will be 45 degree
if we consider (-2+2i) then it will be -45 degree but angle will not -45 degree actually we get answer by adding or deducting 180 or some like this i want to know what we have to add or subtract i am confuse about this

also what to do for third and fourth quadrants

i want to know this for Log of complex number and Polar form

urduworld said:
hi PF

consider (2+1i) then Tan^-1(2/2) which will be 45 degree
if we consider (-2+2i) then it will be -45 degree but angle will not -45 degree actually we get answer by adding or deducting 180 or some like this i want to know what we have to add or subtract i am confuse about this
You seem to be confused between the reference angle and the angle as measured from the positive real axis. For 2 + 2i, the reference angle and the angle itself are both 45 degrees, or pi/4. For -2 + 2i, the reference angle is also 45 degrees (not -45 degrees), but since the angle is in the second quadrant, the actual angle is 180 - 45 = 135 degrees, or 3pi/4. If you calculate the angle using the inverse tangent function, you have t-1(-2/2) = -45 degrees. You have to add 180 degrees to this, because your angle is in the 2nd quadrant, so you get 180 + (-45) = 135 degrees again.

The range of the inverse tangent function is (-90, 90) (in degrees), or (-pi/2, pi/2), so if your angle is not in the 1st or 4th quadrants you have to adjust the value to get the angle you need.

If your angle is in the third quadrant, as it is for -2 - 2i, you'll have tan-1(-2/(-2)) = 45 degrees. The actual angle is 180 + 45 = 225 degrees, or 5pi/4.
urduworld said:
also what to do for third and fourth quadrants

i want to know this for Log of complex number and Polar form

Last edited:
this means i have to add 180 in all the condition except if it is in first

I didn't talk about a fourth quadrant angle, but maybe you can figure out what you need to do. If z = 2 - 2i, the argument would be -45 degrees. As a positive angle, what would it be?

## 1. What is the argument of a complex number?

The argument of a complex number is the angle that the complex number forms with the positive real axis on the complex plane. It is typically measured in radians or degrees and can be thought of as the direction of the vector representing the complex number.

## 2. How do you find the argument of a complex number?

The argument of a complex number can be found using the formula arctan(b/a), where a is the real part of the complex number and b is the imaginary part. This formula can also be written as arctan(y/x), where x and y are the coordinates of the complex number on the complex plane.

## 3. Can the argument of a complex number be negative?

Yes, the argument of a complex number can be negative. This occurs when the complex number falls in the third or fourth quadrant of the complex plane, where the angle is measured clockwise from the positive real axis.

## 4. How do you represent the argument of a complex number in mathematical notation?

The argument of a complex number is typically represented using the Greek letter theta (θ). This notation is usually written as arg(z), where z is the complex number in question.

## 5. What is the range of values for the argument of a complex number?

The range of values for the argument of a complex number is between -π and π radians, or -180° and 180° in degrees. This is because the complex plane is periodic, meaning that any angle greater than 180° can be represented by a smaller angle in the range of -π to π.

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