Forgetting my inverse tangent, polar form of compelx number ASTC

In summary, The polar form of 2i - 1 is r(cosθ + isinθ), where r = √(a2 + b2), θ = arctan(-2), and the correct value of θ can be determined by looking at the original complex number (-1,2).
  • #1
thomas49th
655
0

Homework Statement


Find the polar form of 2i − 1


Finding polar form is easy r(cosx + isinx)

call the real part a and imaginary part b

r = sqrt(a+b)

theta = arctan (-2) = - 63.43

This is the wrong angle for theta as it's 116.57 (which is 180 - 64.43), and I guess this if form that quadrant thing

S | A
___|___
|
T | C


okay not the best grid, but can anyone refresh my memory as how to get the correct value of theta?

Thanks :)
 
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  • #2
Hi thomas49th! :smile:

(have a theta: θ and a square-root: √ :wink:)

(and you meant √(a2 + b2))


Yes, your table shows what's positive (sin, tan, cos, or all) …

(it works because cos*tan = sin, so an even number must be negative, so either 1 or all 3 must be positive :wink:)

so arctan(-2) can be either top left or bottom right, you can't tell which by looking at it

you have to go back to the original 2i - 1, which is at (-1,2), so it's obviously top left! :smile:
 

Related to Forgetting my inverse tangent, polar form of compelx number ASTC

What is the inverse tangent function?

The inverse tangent function, denoted as arctan or tan-1, is the inverse operation of the tangent function. It takes in a ratio of two sides of a right triangle and returns the angle in radians.

What is the polar form of a complex number?

The polar form of a complex number is a way to represent a complex number in terms of its magnitude and angle. It is represented as z = r(cosθ + isinθ), where r is the magnitude and θ is the angle.

How do you use ASTC to remember the signs of the inverse tangent?

ASTC stands for All Students Take Calculus, and it is a mnemonic device used to remember the signs of the inverse trigonometric functions, including inverse tangent. It stands for All, Sine, Tangent, Cosine, which represents the sign of the function in each quadrant of the unit circle.

What is the relationship between the inverse tangent and the tangent function?

The inverse tangent function is the inverse operation of the tangent function. This means that if you take the inverse tangent of a value, and then take the tangent of that result, you will get back the original value.

How can I calculate the inverse tangent of a complex number in polar form?

To calculate the inverse tangent of a complex number in polar form, you can use the formula tan-1(y/x) = arctan(y/x). This will give you the angle in radians of the complex number.

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