PedroB said:Homework Statement
Let tan(q) with q ε ℂ be defined as the natural extension of tan(x) for real values
Find all the values in the complex plane for which |tan(q)| = ∞
Homework Equations
Expressing tan(q) as complex exponentials:
(e^iq - e^(-iq))/i(e^iq + e^(-iq))
The Attempt at a Solution
I really have no idea how to get around this problem. No matter what I equate 'q' to I don't seem to get a valid answer. Any help would be greatly appreciated.
PedroB said:Ok, so I get q= ∏/2 (which makes sense since tan(∏/2)= ∞), but what does this mean exactly? Are the range of values when x + iy = ∏/2? Surely this simply leads to x = ∏/2 which is evidently not a 'range' of values. This is the simpler of problems that I need to do, though it's the one that's given me more trouble (I've got a few complex derivatives questions which were pretty straight forward to me compared to this, strangely enough)
In complex algebra, tangent is defined as the ratio of the sine and cosine of an angle. It is represented by the symbol tan.
Complex algebra is used in trigonometry to solve equations and problems involving complex numbers, which are numbers that have both real and imaginary components. Trigonometric functions such as sine, cosine, and tangent can be expressed in terms of complex numbers.
In complex algebra, the relationship between tangent and cotangent is that they are reciprocals of each other. This means that the tangent of an angle is equal to the inverse of the cotangent of the same angle.
To find the values of tangent in complex algebra, you can use the Pythagorean identity, which states that tan^2θ + 1 = sec^2θ. This can help you solve for the tangent of an angle using the values of sine and cosine.
Yes, complex numbers can be used in trigonometric identities involving tangent. In fact, many trigonometric identities involving tangent are derived using complex numbers and their properties.