(1 + i) a=1 , b=1 ; $\left| z \right| = \sqrt{a^{2} + b^{2}}$ = $\sqrt{1^{2} + 1^{2}}$=$\sqrt{2}$ ; cos α = $\frac{a}{|z|}$=$\frac{1}{\sqrt{2}}$=$\frac{\sqrt{2}}{2}$ ; sin α = $\frac{b}{|z|}$=$\frac{1}{\sqrt{2}}$=$\frac{\sqrt{2}}{2}$ => α=45◦ => $\frac{\pi}{4}$	(-1 - i) a=-1 , b=-1 ; $\left| z \right| = \sqrt{a^{2} + b^{2}}$ = $\sqrt{{( - 1)}^{2} + ({- 1)}^{2}}$=$\sqrt{2}$ ; cos α = $\frac{a}{|z|}$=$\frac{- 1}{\sqrt{2}}$=$- \frac{\sqrt{2}}{2}$ ; sin α = $\frac{b}{|z|}$=$\frac{- 1}{\sqrt{2}}$=$- \frac{\sqrt{2}}{2}$ => α=225◦ =>180◦+45◦ => $\frac{5}{4}\ \pi$
(1 - i) a=1 , b=-1 ; $\left| z \right| = \sqrt{a^{2} + b^{2}}$ = $\sqrt{1^{2} + ({- 1)}^{2}}$=$\sqrt{2}$ ; cos α = $\frac{a}{|z|}$=$\frac{1}{\sqrt{2}}$=$\frac{\sqrt{2}}{2}$ ; sin α = $\frac{b}{|z|}$=$\frac{- 1}{\sqrt{2}}$=$- \frac{\sqrt{2}}{2}$ => α=315◦ =>360◦-45◦ => $\frac{7}{4}\ \pi$	(-1 + i) a=-1 , b=+1 ; $\left| z \right| = \sqrt{a^{2} + b^{2}}$ = $\sqrt{{( - 1)}^{2} + 1^{2}}$=$\sqrt{2}$ ; cos α = $\frac{a}{|z|}$=$\frac{- 1}{\sqrt{2}}$=$- \frac{\sqrt{2}}{2}$ ; sin α = $\frac{b}{|z|}$=$\frac{1}{\sqrt{2}}$=$\frac{\sqrt{2}}{2}$ => α=135◦ =>180◦-45◦ => $\frac{3}{4}\ \pi$
(1 + $\sqrt{\mathbf{3}}$i) a=1 , b=$\sqrt{3}$ ; $\left| z \right| = \sqrt{a^{2} + b^{2}}$ = $\sqrt{1^{2} + {(\sqrt{3})}^{2}}$=$\sqrt{4}$=2 ; cos α = $\frac{a}{|z|}$=$\frac{1}{2}$ ; sin α = $\frac{b}{|z|}$=$\frac{\sqrt{3}}{2}$ => α=60◦ => $\frac{\pi}{3}$	(-1 - $\sqrt{\mathbf{3}}$i) a=-1 , b=$- \sqrt{3}$ ; $\left| z \right| = \sqrt{a^{2} + b^{2}}$ = $\sqrt{{( - 1)}^{2} + {( - \sqrt{3})}^{2}}$=$\sqrt{4}$=2 ; cos α = $\frac{a}{|z|}$=$- \frac{1}{2}$ ; sin α = $\frac{b}{|z|}$=$- \frac{\sqrt{3}}{2}$ => α=240◦=>180◦+60◦ => $\frac{4}{3}\ \pi$
(-1 + $\sqrt{\mathbf{3}}$i) a=-1 , b=$\sqrt{3}$ ; $\left| z \right| = \sqrt{a^{2} + b^{2}}$ = $\sqrt{{( - 1)}^{2} + {(\sqrt{3})}^{2}}$=$\sqrt{4}$=2 ; cos α = $\frac{a}{|z|}$=$- \frac{1}{2}$ ; sin α = $\frac{b}{|z|}$=$\frac{\sqrt{3}}{2}$ => α=120◦=>180◦-60◦ => $\frac{2}{3}\ \pi$	(1 - $\sqrt{\mathbf{3}}$i) a=1 , b=$- \sqrt{3}$ ; $\left| z \right| = \sqrt{a^{2} + b^{2}}$ = $\sqrt{1^{2} + {( - \sqrt{3})}^{2}}$=$\sqrt{4}$=2 ; cos α = $\frac{a}{|z|}$= $\frac{1}{2}$ ; sin α = $\frac{b}{|z|}$=$- \frac{\sqrt{3}}{2}$ => α=300◦=>360◦-60◦ => $\frac{5}{3}\ \pi$
($\sqrt{\mathbf{3}}$ + i) a=$\sqrt{3}$ , b=1; $\left| z \right| = \sqrt{a^{2} + b^{2}}$ = $\sqrt{{(\sqrt{3})}^{2} + 1^{2}}$=$\sqrt{4}$=2 ; cos α = $\frac{a}{|z|}$=$\frac{\sqrt{3}}{2}$ ; sin α = $\frac{b}{|z|}$=$\frac{1}{2}$ => α=30◦ => $\frac{\pi}{6}$	($\mathbf{-}\sqrt{\mathbf{3}}$ - i) a=$- \sqrt{3}$ , b=-1; $\left| z \right| = \sqrt{a^{2} + b^{2}}$ = $\sqrt{{( - \sqrt{3})}^{2} + {( - 1)}^{2}}$=$\sqrt{4}$=2 ; cos α = $\frac{a}{|z|}$=$- \frac{\sqrt{3}}{2}$ ; sin α = $\frac{b}{|z|}$=$- \frac{1}{2}$ => α=210◦=>180◦+30◦ => $\frac{7}{6}\ \pi$
($\mathbf{-}\sqrt{\mathbf{3}}$ + i) a=$- \sqrt{3}$ , b=1; $\left| z \right| = \sqrt{a^{2} + b^{2}}$ = $\sqrt{{( - \sqrt{3})}^{2} + 1^{2}}$=$\sqrt{4}$=2 ; cos α = $\frac{a}{|z|}$=$- \frac{\sqrt{3}}{2}$ ; sin α = $\frac{b}{|z|}$=$\ \frac{1}{2}$ => α=150◦=>180◦-30◦ => $\frac{5}{6}\ \pi$	($\sqrt{\mathbf{3}}$ - i) a=$\sqrt{3}$ , b=-1; $\left| z \right| = \sqrt{a^{2} + b^{2}}$ = $\sqrt{{(\sqrt{3})}^{2} + {( - 1)}^{2}}$=$\sqrt{4}$=2 ; cos α = $\frac{a}{|z|}$=$- \frac{\sqrt{3}}{2}$ ; sin α = $\frac{b}{|z|}$=$- \frac{1}{2}$ => α=330◦=>360◦-30◦ => $\frac{11}{6}\ \pi$