Find ${\left(-2\sqrt{3}-2i\right)}^6$ and write the result in the form $a+bi$.

Use De Moivre's theorem to find ${\left[5\left(\cos 35^{\circ }+i\sin 35^{\circ }\right)\right]}^5$ in trigonometric form, with the argument on $\left[0^{\circ },360^{\circ }\right)$.

The three cube roots of $8\left(\cos 30^{\circ }+i\sin 30^{\circ }\right)$ are each written with an argument on $\left[0^{\circ },360^{\circ }\right)$. Which one has the smallest argument?

The four fourth roots of $81\left(\cos 250^{\circ }+i\sin 250^{\circ }\right)$ are found by De Moivre's theorem. What modulus does each of the roots have?

The three cube roots of $64\left(\cos 300^{\circ }+i\sin 300^{\circ }\right)$ are each written with an argument on $\left[0^{\circ },360^{\circ }\right)$. Which one has the smallest argument?

The nine ninth roots of a complex number are plotted in the complex plane. What angle separates one root from the next one around the circle?

Find ${\left(-\sqrt{2}+i\sqrt{2}\right)}^6$ and write the result in the form $a+bi$.

The ten tenth roots of a complex number are plotted in the complex plane. What angle separates one root from the next one around the circle?

The two square roots of $9\left(\cos 150^{\circ }+i\sin 150^{\circ }\right)$ are each written with an argument on $\left[0^{\circ },360^{\circ }\right)$. Which one has the smallest argument?

Find ${\left(-1-i\sqrt{3}\right)}^6$ and write the result in the form $a+bi$.

The three cube roots of $8\left(\cos 200^{\circ }+i\sin 200^{\circ }\right)$ are found by De Moivre's theorem. What modulus does each of the roots have?

Use De Moivre's theorem to find ${\left[5\left(\cos 70^{\circ }+i\sin 70^{\circ }\right)\right]}^3$ in trigonometric form, with the argument on $\left[0^{\circ },360^{\circ }\right)$.

The four fourth roots of $1296\left(\cos 40^{\circ }+i\sin 40^{\circ }\right)$ are found by De Moivre's theorem. What modulus does each of the roots have?

The five fifth roots of $3125\left(\cos 270^{\circ }+i\sin 270^{\circ }\right)$ are each written with an argument on $\left[0^{\circ },360^{\circ }\right)$. Which one has the smallest argument?

Use De Moivre's theorem to find ${\left[4\left(\cos 100^{\circ }+i\sin 100^{\circ }\right)\right]}^4$ in trigonometric form, with the argument on $\left[0^{\circ },360^{\circ }\right)$.

The two square roots of a complex number are plotted in the complex plane. What angle separates one root from the next one around the circle?

Use De Moivre's theorem to find ${\left[4\left(\cos 145^{\circ }+i\sin 145^{\circ }\right)\right]}^5$ in trigonometric form, with the argument on $\left[0^{\circ },360^{\circ }\right)$.

Use De Moivre's theorem to find ${\left[3\left(\cos 10^{\circ }+i\sin 10^{\circ }\right)\right]}^5$ in trigonometric form, with the argument on $\left[0^{\circ },360^{\circ }\right)$.

Find ${\left(-2\sqrt{3}+2i\right)}^5$ and write the result in the form $a+bi$.

Use De Moivre's theorem to find ${\left[5\left(\cos 110^{\circ }+i\sin 110^{\circ }\right)\right]}^6$ in trigonometric form, with the argument on $\left[0^{\circ },360^{\circ }\right)$.