Checking imaginary problems with numbers

[onthesnap55]

How do I check x^4 - 81=0
When x=3i

 

[skeeter]

note that ...
i[sup:1od9lyn7]1[/sup:1od9lyn7] = i
i[sup:1od9lyn7]2[/sup:1od9lyn7] = -1
i[sup:1od9lyn7]3[/sup:1od9lyn7] = -i
i[sup:1od9lyn7]4[/sup:1od9lyn7] = 1

the pattern cycles for higher powers of i

(3i)[sup:1od9lyn7]4[/sup:1od9lyn7] - 81 = 3[sup:1od9lyn7]4[/sup:1od9lyn7]i[sup:1od9lyn7]4[/sup:1od9lyn7] - 81 = 81*1 - 81 = 0

 

[stapel]

How do I check x^4 - 81=0 When x=3i

Plug "3i" in for "x", subtract 81 from the result, and check that you do indeed end up with zero!

Eliz.