# 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.

Please see the attached file for the fully formatted problems.

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#### Solution Summary

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

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