How do I convert c=9e^((-5/2)∏j) to component notation?

[Sastronaut]

Homework Statement

Convert the following to component notation:

c=9e^((-5/2)∏j)

Homework Equations

The Attempt at a Solution

I am not very sure how to approach this problem...recently in my electronics course we discussed how we can us real and imaginary numbers and complex math...any help would be greatly appreciated; just a point in the right direction to get me started on the problem. thanks pf!

 

[voko]

Euler's formula - ring a bell?

 

[Sastronaut]

that's a negative ghost rider...could you explain further voko? :)

 

[voko]

http://en.wikipedia.org/wiki/Euler's_formula

 

[Nickie]

To convert c=9e^((-5/2)∏j) to component notation, we need to express the complex number in terms of its real and imaginary components. The given expression can be rewritten as c = 9(cos(-5π/2) + j*sin(-5π/2)). From Euler's formula, we know that e^(ix) = cos(x) + j*sin(x). Therefore, we can rewrite the expression as c = 9e^(j(-5π/2)). This represents a complex number with a magnitude of 9 and an angle of -5π/2, or 270 degrees, in polar form.

To convert this to component notation, we can use the trigonometric identities cos(-x) = cos(x) and sin(-x) = -sin(x). This gives us c = 9(cos(5π/2) - j*sin(5π/2)). Simplifying further, we get c = 9(0 - j*(-1)) = 9j. Therefore, the component notation of c=9e^((-5/2)∏j) is 9j.