tiny-tim said:Hi icystrike!
Your first answer, eπi/3, would be the correct answer for +1/2 (1 + i√3).
So, to get minus that, multiply by … ?
For the second answer, the ekπi/2 can be simplified a little, for example by using a "±" (and of course, put the 2 on the other side).
tiny-tim said:uhh?
Hint: e? = -1 ?
tiny-tim said:Yup! … so instead of eiπ/3, it's … ?
… it's only a fifth-order equation! To express a complex equation in the form of e^(iθ), you need to convert all the terms to their polar form. Then, you can use Euler's formula e^(iθ) = cos(θ) + isin(θ) to write the equation in the desired form.
e^(iθ) is a crucial component in solving complex equations because it allows us to represent complex numbers in a simplified form. It also helps in performing operations like multiplication, division, and powers on complex numbers more easily.
Yes, e^(iθ) can be used to solve any complex equation. It is a powerful tool that simplifies the calculations and gives a better understanding of the solutions to complex problems.
The value of e^(iθ) corresponds to a point on the unit circle in trigonometry, where θ is the angle formed by the point and the positive x-axis. This connection between e^(iθ) and the unit circle is the basis of Euler's formula.
Yes, complex equations can be expressed in different forms, such as rectangular form (a + bi), polar form (r(cosθ + isinθ)), and exponential form (re^(iθ)). However, e^(iθ) is the most commonly used form due to its simplicity and utility in solving complex equations.