#Complex numbers

16 messages · Page 1 of 1 (latest)

tame epoch
#

My initial idea was to turn that complex number into Euler form: √6 ⋅ e^(-πi/4)

Then since it's a triangle, it must have 3 vertices so multiply by w and w^2 where w = e^(2πi/3) to find the two other vertices.

#

However, I am wrong and I think it has something to do with the equilateral including O in the triangle, can someone help

rancid depot
#

I'd draw an argand diagram first to visualise it

#

So to get b you need its r and its argument

#

And you know that the triangle is equilateral so all sides are equal and you have A given

#

So the r of B must be equal to the r of A

#

use pythagoras to get that

#

Now to get the argument you know that all angles in an equilateral are 60

#

You'll need to get the argument of A first which is –45 degrees

#

So on your diagram you'll see that for the angle AOB to be 60 you must go above the real axis 15 degrees or move from the negative Imaginary axis 45 degrees ACW or to the left

#

You can now easily get the argument of B

#

And you have its r

#

@tame epoch

#

Obvi you should work in radians not degrees

tame epoch
#

Thanks, it makes sense