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Magazine Problem 4
Find the fifth roots of \(-3+i 3\) in polar form and in exponential form.
Problem 5
Find the three cube roots of \(8\left(\cos 264^{\circ}+j \sin 264^{\circ}\right)\) and state which of them is the principal cube root. Show all three roots on an Argand diagram.
Problem 7
Find the fifth roots of \(-1\), giving the results in polar form. Express the princibal root in the form re \(^{\text {kt }}\),
Problem 7
Fxpress \(\cos ^{4} \theta\) in terms of cosines of multiples of \(\theta\).
Problem 8
Determine the roots of the equation \(x^{3}+64=0\) in the form \(a+j b\), where \(a\) and \(b\) are real.
Problem 10
Show that the equation \(z^{3}=1\) has one real root and two other roots which are not real, and that, if one of the non-real roots is denoted by w, the other is then \(w^{2}\). Mark on the Argand diagram the points which represent the three roots and show that they are the vertices of an equilateral triangle.
