<![CDATA[Math Is Fun Forum / Maths]]> 2020-10-07T10:27:02Z FluxBB https://www.mathisfunforum.com/viewtopic.php?id=25883 <![CDATA[Re: Maths]]> hi Pema,

Welcome to the forum.

Thanks to zetafunc for the initial hint.

You might also find the following useful:

w^2 + w + 1 = 0  =>  w + 1 = - w^2

You can prove this equation either by substituting the complex values for each root (the working is identical) or like this:

Let w^2 + w + 1 = z ; then w^3 + w^2 + w = wz

As w^3 = 1 we end up with z = wz.  So either z = 0 or w = 1.  As we know that second isn't the case z must be 0.

Bob

]]>
https://www.mathisfunforum.com/profile.php?id=67694 2020-10-07T10:27:02Z https://www.mathisfunforum.com/viewtopic.php?pid=415282#p415282
<![CDATA[Re: Maths]]> Hi Pema,

What do you get when you add A and B together?

What kind of matrix is it, and what do we know about powers of these matrices?

]]>
https://www.mathisfunforum.com/profile.php?id=206089 2020-10-07T08:57:56Z https://www.mathisfunforum.com/viewtopic.php?pid=415281#p415281
<![CDATA[Maths]]> If w is an imaginary cube root of unity and A =[ 1  0    , B= ( w 0   then
0  w].           0  1)                   (A+B) ^103 is equal to

]]>
2020-10-07T05:30:08Z https://www.mathisfunforum.com/viewtopic.php?pid=415278#p415278