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I do not understand this topic and particularly this example. In the class the result was found out but I still do not get it. How did the teacher came up with this outcome?

Firstly please show me what was the topic and the example in class. Given the topic I will provide the answer and the easiest way to complete it. For example, let's say the student had to solve the equation ...
MF
2937 Views

Use de Moivre's theorem to calculate an expression for sin(5x) in terms of sin(x) only.

de Moivre's theorem gives us that (cos(x) + i sin(x)) n = cos(nx) + i sin(nx), for integers n and real values x.Therefore cos(5x) + i sin(5x) = (cos(x) + i sin(x)) 5 = cos 5 (x) + 5i cos 4 (x)sin(x) - 10 cos...
CB
38637 Views

Use de Moivre’s theorem to show that, (sin(x))^5 = A sin(5x) + Bsin(3x) + Csin(x), where A , B and C are constants to be found.

State de Moivre's theorem. Use n =5 and solve. I'll show this on the whiteboard.
RM
6790 Views

Find all of the roots of unity, Zn, in the case that (Zn)^6=1

Here we use the complex exponential form of 1 which is e^(i 2n pi). Applying the sixth root and substituting in for integer values of n gives all roots in complex exponential form.These can be converted into...
CR
3349 Views

How can we describe complex numbers ?

The simplest way to describe a complex number is by its real and imaginary part, z=x+yi, this may be wrote as Re(z)=x and Im(z)=y. These complex numbers follow the same rules as normal algebra, that is we ca...
TL
3321 Views