Complex Numbers identity help

[lunds002]

Homework Statement

Let z1 = a (cos (pi/4) + i sin (pi/4) ) and z2 = b (cos (pi/3) + i sin (pi/3))
Express (z1/z2)^3 in the form z = x + yi.

]2. Homework Equations [/b]

The Attempt at a Solution

a(cos (pi/4) + i sin (pi/4))
b (cos (pi/3) + i sin (pi/3))

I then multiplied the top and bottom by the bottom reciprocal : cos (pi/3) - i sin (pi/3) to get

a(cos (pi/4) x cos (pi/3) + sin (pi/4) sin (pi/3)) + i (sin (pi/4) x cos (pi/3) - sin (pi/3) x cos (pi/4)

 

[rock.freak667]

Do you know the identity e^iθ=cosθ+isinθ?

It will make your calculations easier since you can express it in terms of the exponential function.

 

[lunds002]

right, i forget that. thank you

 

[thornluke]

I'm not sure if I'm right, I am stuck on this question as well.

I got z=(√2)a³/2b³ - (√2)a³/2b³ i

 

[vela]

That's right.

 

[thornluke]

That's right.

That's great. I'm still kind of new to this topic, still not confident with it and I have an unit test coming up in less than a week's time!