Question: Consider the question in the image given. 2. (a) Show that if z E C satisfies 22 + V3 z + 3 =0, then 23

Consider the question in the image given.

2. (a) Show that if z E C satisfies 22 + V3 z + 3 =0, then 23 = 3V3. (b) Suppose that A E MA(C) has characteristic polynomial PA(a) = (202 + 3) (202 + V3 x + 3). Find A 2. You may use the fact that A is a 4 x 4 matrix with 4 distinct complex eigenvalues and is therefore diagonalizable over C

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