Understanding Complex Plane and Finding Arguments: A Scientist's Perspective

In summary, the conversation discusses the difficulty in finding the argument for the given equations, specifically in relation to the use of tangent. The answer booklet suggests using a negative value for tangent, possibly due to the presence of an imaginary component in the solution. The individual believes they can solve the problem after this clarification.
  • #1
SUSUSUSUSUSUSUSU

Homework Statement


The picture below.

Homework Equations


cos2x=1-2sinx
sin2x= 2sinxcosx

The Attempt at a Solution



I got the modulus by using the Pythagoras theorem which is 2sin theta

But I faced difficulty to find the argument. I have no idea why i end up with tan a (alpha) = cot theta which is not the right answer. on the answer booklet, it's written that it is tan a = -cot theta. I do not understand that why it comes to negative...? I just did tan a = sin2x/(1-cos2x) = cot x. Is it just because it is -isin2x?I think after that i can solve it.

Thank you.
 

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  • #2
SUSUSUSUSUSUSUSU said:

Homework Statement


The picture below.

Homework Equations


cos2x=1-2sinx
sin2x= 2sinxcosx

The Attempt at a Solution



I got the modulus by using the Pythagoras theorem which is 2sin theta

But I faced difficulty to find the argument. I have no idea why i end up with tan a (alpha) = cot theta which is not the right answer.
on the answer booklet, it's written that it is tan a = -cot theta. I do not understand that why it comes to negative...? I just did tan a = sin2x/(1-cos2x) = cot x. Is it just because it is -isin2x?
Yes. The imaginary component is ##-\sin(2\theta)##.
SUSUSUSUSUSUSUSU said:
I think after that i can solve it.

Thank you.
 

FAQ: Understanding Complex Plane and Finding Arguments: A Scientist's Perspective

What is a complex plane?

A complex plane, also known as an Argand diagram, is a graphical representation of complex numbers. It consists of a horizontal axis representing the real part of a complex number and a vertical axis representing the imaginary part.

How do you plot a complex number on a complex plane?

To plot a complex number on a complex plane, you can use the coordinates of the number's real and imaginary parts. For example, the complex number 3 + 4i would be plotted at the point (3,4) on the complex plane.

What is the purpose of a complex plane?

The complex plane is used to visualize and manipulate complex numbers in a geometric way. It allows for easier understanding and computation of complex numbers, which have important applications in mathematics, physics, and engineering.

What does the distance from the origin on a complex plane represent?

The distance from the origin on a complex plane represents the absolute value, or modulus, of a complex number. It can also be thought of as the magnitude or size of the complex number.

How do you perform operations on complex numbers using a complex plane?

To perform operations on complex numbers using a complex plane, you can use the geometric properties of the complex plane. Addition and subtraction can be done by adding or subtracting the real and imaginary parts separately, and multiplication and division can be done using polar coordinates and trigonometric functions.

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