# Expressing complex function in standard rectangular form

• elimenohpee
In summary, the conversation discusses transforming a complex function in exponential form into standard Cartesian form. The individual is unsure if their method is correct, but it is confirmed that it is. The discussion also mentions the difficulty in transforming it back to the original form, which is due to the fact that the original form is not in polar form.
elimenohpee
I'm given a complex function in the exponential form:

2.5j e^(-j40*pi)

Transforming this into the standard Cartesian form is pretty straight forward, but the extra j multiplying the 2.5 is kind of throwing me off. I don't know if I did it right, but this is what I did:

2.5j (cos[-40pi] + jsin[-40pi]) = 2.5j (cos[40pi] - jsin[40pi]) = 2.5j (1-0) = 2.5j

Is that correct? I don't know if it is or not, because I don't see how you could transform it back into the original form after putting it into Cartesian form. Thanks

elimenohpee said:
I'm given a complex function in the exponential form:

2.5j e^(-j40*pi)

Transforming this into the standard Cartesian form is pretty straight forward, but the extra j multiplying the 2.5 is kind of throwing me off. I don't know if I did it right, but this is what I did:

2.5j (cos[-40pi] + jsin[-40pi]) = 2.5j (cos[40pi] - jsin[40pi]) = 2.5j (1-0) = 2.5j

Is that correct? I don't know if it is or not, because I don't see how you could transform it back into the original form after putting it into Cartesian form. Thanks

Looks right to me. Is there a way to check the answer?

elimenohpee said:
I'm given a complex function in the exponential form:

2.5j e^(-j40*pi)

Transforming this into the standard Cartesian form is pretty straight forward, but the extra j multiplying the 2.5 is kind of throwing me off. I don't know if I did it right, but this is what I did:

2.5j (cos[-40pi] + jsin[-40pi]) = 2.5j (cos[40pi] - jsin[40pi]) = 2.5j (1-0) = 2.5j

Is that correct? I don't know if it is or not, because I don't see how you could transform it back into the original form after putting it into Cartesian form. Thanks

Yes that's correct

If you are having difficulty transforming it into the original form, it is probably because the original form is not really the polar form.

The polar form of 2.5j is 2.5e^(j*pi/2) but that is equivalent to the original expression since e^(-j*40pi)=e^0=1 (since the complex exponential has a period of 2pi).

Ok good :)

Such an odd question, I guess it was more or less to try and throw you off.

## 1. What is a complex function?

A complex function is a mathematical function that maps complex numbers to complex numbers. It can be expressed in the form of f(z) = u(x,y) + iv(x,y), where u and v are real-valued functions of the complex variable z = x + iy and i is the imaginary unit.

## 2. What is standard rectangular form?

Standard rectangular form, also known as the Cartesian form, is a way of representing a complex number in the form z = x + iy, where x and y are real numbers and i is the imaginary unit. This form is useful for performing mathematical operations on complex numbers.

## 3. How do you express a complex function in standard rectangular form?

To express a complex function in standard rectangular form, you first need to identify the real and imaginary parts of the function. Then, you can combine these parts using the complex variable z = x + iy to get the function in the form f(z) = u(x,y) + iv(x,y).

## 4. What are the advantages of expressing a complex function in standard rectangular form?

Expressing a complex function in standard rectangular form allows for easier manipulation and calculation of the function. It also makes it easier to visualize the function on the complex plane, as the real part represents the horizontal axis and the imaginary part represents the vertical axis.

## 5. Can all complex functions be expressed in standard rectangular form?

Yes, all complex functions can be expressed in standard rectangular form. This form is the most commonly used and widely accepted way of representing complex numbers and functions.

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