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. In this question, i ? C is the imaginary unit, that is, the complex number...

. In this question, i ? C is the imaginary unit, that is, the complex number satisfying i^2 = ?1. (a) Verify that 2 ? 3i is a root of the polynomial f(z) = z^4 ? 7z^3 + 27z^2 ? 47z + 26 Find all the other roots of this polynomial. (b) State Euler’s formula for e^i? where ? is a real number. (c) Use Euler’s formula to prove the identity cos(2?) = cos^2 ? ? sin^2 ? (d) Find all solutions to z^3 = 1 in both polar form (z = re^i?, where r > 0 and 0 ? ? < 2? are real numbers) and rectangular form (z = a + ib, where a and b are real numbers).

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