Question 1.29: Find each of the indicated roots and locate them graphically...

(a) (-1+i)^{1 / 3}

If k=0, z_1=2^{1 / 6}(\cos \pi / 4+i \sin \pi / 4).
If k=1, z_2=2^{1 / 6}(\cos 11 \pi / 12+i \sin 11 \pi / 12).
If k=2, z_3=2^{1 / 6}(\cos 19 \pi / 12+i \sin 19 \pi / 12).

These are represented graphically in Fig. 1-32.

(b) (-2 \sqrt{3}-2 i)^{1 / 4}

If k=0, z_1=\sqrt{2}(\cos 7 \pi / 24+i \sin 7 \pi / 24).
If k=1, z_2=\sqrt{2}(\cos 19 \pi / 24+i \sin 19 \pi / 24).
If k=2, z_3=\sqrt{2}(\cos 31 \pi / 24+i \sin 31 \pi / 24).
If k=3, z_4=\sqrt{2}(\cos 43 \pi / 24+i \sin 43 \pi / 24)

These are represented graphically in Fig. 1-33.