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Complex Roots and Solutions, De Moivre's Theorem and Argand Diagrams

1 Find the real and complex solutions of these cubic equations.
a) (z-3)(z2-5z+8)=0
b) z3 - 10z2- 34z- 40 = 0, given that 3-i is a root (solution).
2 Solve the equation z3 = 125 cis 45
3 Consider the complex number: z =
= cos + z sin
a) Use De Moivre's theorem to find z2, z4 and z6. Leave your answers in polar form.
b) Plot z2, z4, z6 on an Argand diagram.

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Complex Roots and Solutions, De Moivre's Theorem and Argand Diagrams are investigated. The solution is detailed and well presented.

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