unchained1978 said:This is related to another post of mine. How would you go about writing [itex]\frac{1}{e^{z}-1}[/itex] in u+iv form? Usually multiplying through with the complex conjugate gives you the desired form, but here I'm not sure that it works. Any suggestions?
unchained1978 said:This is related to another post of mine. How would you go about writing [itex]\frac{1}{e^{z}-1}[/itex] in u+iv form? Usually multiplying through with the complex conjugate gives you the desired form, but here I'm not sure that it works. Any suggestions?
The purpose of writing a function in u+iv form is to represent complex numbers in a mathematical expression. This form is also known as the Cartesian form or rectangular form, and it allows for easier computation and visualization of complex numbers.
To convert a function from standard form (a+bi) to u+iv form, you can use the following formula: u+iv = a+bi, where u = Re(z) and v = Im(z). This means that the real part of the complex number is written as 'u' and the imaginary part is written as 'iv'.
Yes, a function can be written in both u+iv form and polar form. These are two different ways of representing complex numbers, with u+iv form using rectangular coordinates and polar form using polar coordinates. The conversion between these two forms can be done using trigonometric functions.
To use u+iv form to perform calculations with complex numbers, you can follow the same rules as for real numbers. For addition and subtraction, you simply add or subtract the real and imaginary parts separately. For multiplication, you use the FOIL method and simplify the terms. For division, you multiply the numerator and denominator by the complex conjugate of the denominator.
One limitation of using u+iv form is that it does not work for all types of complex numbers. For example, it cannot represent numbers with a negative square root. In addition, it may become more complicated to perform calculations with complex numbers in u+iv form if the expressions become very complex.