Chapter 7.3, Problem 3E

(a)

To determine

The value of ${\left(\sqrt{3}+i\right)}^7$ in standard form by using De Moivre’s Theorem.

(b)

To determine

The value of ${\left(\frac{\sqrt{3}}{2}+\frac{1}{2}i\right)}^{21}$ in standard form by using De Moivre’s Theorem.

(c)

To determine

The value of ${\left(-\sqrt{3}+i\right)}^{10}$ in standard form by using De Moivre’s Theorem.

(d)

To determine

The value of ${\left(\frac{\sqrt{3}}{2}-\frac{1}{2}i\right)}^{18}$ in standard form by using De Moivre’s Theorem.

(e)

To determine

The value of ${\left(-\frac{1}{2}+\frac{\sqrt{3}}{2}i\right)}^{18}$ in standard form by using De Moivre’s Theorem.

(f)

To determine

The value of ${\left(\sqrt{2}+\sqrt{2}i\right)}^9$ in standard form by using De Moivre’s Theorem.

(g)

To determine

The value of ${\left(1-\sqrt{3}i\right)}^8$ in standard form by using De Moivre’s Theorem.

(h)

To determine

The value of ${\left(-\frac{1}{2}+\frac{\sqrt{3}}{2}i\right)}^{12}$ in standard form by using De Moivre’s Theorem.