Complex Number proof??? (1 Viewer)

[Michaelmoo]

Ok in teh Fitzpatrick test book, there are a few "show" questions which to me seem quite ridiculous; ex 31(b) Question 32. e.g.

Show, that for z1,z2 and z3, where z = x + iy

z1(z2.z3) = (z1.z2)z3

Do you simply let z1 = x + iy, z2 = a +ib..... Expand and then collect like terms to prove this???

Thanks.

N.B. .(dot) = times..(x)

 

[Zeber]

lol what's the point of the () 's? it's multiplication so its the same shit. or are you talking about z1|z2.z3| = |z1.z2|.z3?

 

[Michaelmoo]

lol what's the point of the () 's? it's multiplication so its the same shit. or are you talking about z1|z2.z3| = |z1.z2|.z3?

Nope the question is simply like that, ridiculous isnt it

 

[Trebla]

Nope the question is simply like that, ridiculous isnt it

I think that's what you're meant to prove using z_j = x_j + iy_j for j =1,2,3. It is quite trivial.
For the LHS z₁(z₂.z₃) you have to work out the expression of (z₂.z₃) first and then multiply it by z₁.
For the RHS (z₁.z₂)z₃) you have to work out the expression of (z₁.z₂) first and then multiply it by z₃.

This is basically verifying that you can use this brand new number system (the complex number system) with rules similar to that of the real number system.