Verify roots satisfy polynomial equations

A question is this type if and only if it asks to verify or show that a given complex number satisfies a particular polynomial equation by direct substitution.

1 questions · Standard +0.3

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CAIE P3 2011 June Q7
8 marks Standard +0.3
7
  1. Find the roots of the equation $$z ^ { 2 } + ( 2 \sqrt { } 3 ) z + 4 = 0$$ giving your answers in the form \(x + \mathrm { i } y\), where \(x\) and \(y\) are real.
  2. State the modulus and argument of each root.
  3. Showing all your working, verify that each root also satisfies the equation $$z ^ { 6 } = - 64$$