Find the Taylor series expansion of(a) f (z) = 6z + 8(2z + 3)(4z + 5) at z = 1, (b) f (z) = 2i4 + iz at z = −3i
Question
Solution 1
Sure, let's solve this step by step.
(a) f (z) = 6z + 8(2z + 3)(4z + 5) at z = 1
First, simplify the function: f(z) = 6z + 8(2z + 3)(4z + 5) = 6z + 8(8z^2 + 22z + 15) = 6z + 64z^2 + 176z + 120 = 64z^2 + 182z + 120
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