math
posted by Andrea
Is 2+i a solution of z^24z+5=0? Please help!!!!!!! :(

Arora
z^2  4z + 5 = 0
(Note that the square of i is equal to 1)
(2 + i)^2  4(2 + i) + 5
= 4 + (i^2) + 4i  8  4i + 5
= 4  1  8 + 5
= 9  9
= 0
Hence, yes, it is a solution.
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