Math Is Fun Forum

cooljackiec

Member

Registered: 2012-12-13

Posts: 186

complex fun

Find every complex number whose sixth power equals 64.

I tried doing

. That didn't work out

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I see you have graph paper.
You must be plotting something

bobbym

bumpkin

From: Bumpkinland

Registered: 2009-04-12

Posts: 109,606

Re: complex fun

The first thing is that you can see that 2 and -2 are solutions and they are roots of x^6 - 64 = 0

So we can deflate them out of the problem

Now

Now you just solve them as 2 quadratics to get the 4 complex roots.

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In mathematics, you don't understand things. You just get used to them.
If it ain't broke, fix it until it is.
Always satisfy the Prime Directive of getting the right answer above all else.

Bob

Administrator

Registered: 2010-06-20

Posts: 10,621

Re: complex fun

hi cooljackiec

Or you can use modulus argument form to get these.

You can see that one answer is 2.

So draw a circle radius 2 around (0,0) in the Argand diagram.

Starting at (2,0) mark a point every 1/6th of a turn.  This will give all six answers.

Bob

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Children are not defined by school ...........The Fonz
You cannot teach a man anything;  you can only help him find it within himself..........Galileo Galilei
Sometimes I deliberately make mistakes, just to test you!  …………….Bob