118000 What is the value of
\(\left(\frac{i+\sqrt{3}}{-i+\sqrt{3}}\right)^{52722}+\left(\frac{i-\sqrt{3}}{i+\sqrt{3}}\right)^{40305} \text { where } i=\sqrt{-1} \text { ? }\)

117993 If \(a=\cos 2 \alpha+i \sin 2 \alpha, b=\cos 2 \beta+i \sin 2 \beta\), \(c=\cos 2 \gamma+i \sin 2 \gamma\) and \(d=\cos 2 \delta+i \sin 2 \delta\), then
\(\sqrt{\text { abcd }}+\frac{1}{\sqrt{\text { abcd }}}=\)

117994 If \(a=\cos \alpha+i \sin \alpha, b=\cos \beta+i \sin \beta\), \(\mathbf{c}=\cos \gamma+i \sin \gamma\) and \(\frac{\mathbf{b}}{\mathbf{c}}+\frac{\mathbf{c}}{\mathbf{a}}+\frac{\mathbf{a}}{\mathrm{b}}=1\), then \(\cos (\beta-\gamma)+\cos (\gamma-\alpha)+\cos (\alpha-\beta)\) is equal to

117995 One of the values of \(\left(\frac{1+i}{\sqrt{2}}\right)^{2 / 3}\) is

118000 What is the value of
\(\left(\frac{i+\sqrt{3}}{-i+\sqrt{3}}\right)^{52722}+\left(\frac{i-\sqrt{3}}{i+\sqrt{3}}\right)^{40305} \text { where } i=\sqrt{-1} \text { ? }\)

117993 If \(a=\cos 2 \alpha+i \sin 2 \alpha, b=\cos 2 \beta+i \sin 2 \beta\), \(c=\cos 2 \gamma+i \sin 2 \gamma\) and \(d=\cos 2 \delta+i \sin 2 \delta\), then
\(\sqrt{\text { abcd }}+\frac{1}{\sqrt{\text { abcd }}}=\)

117994 If \(a=\cos \alpha+i \sin \alpha, b=\cos \beta+i \sin \beta\), \(\mathbf{c}=\cos \gamma+i \sin \gamma\) and \(\frac{\mathbf{b}}{\mathbf{c}}+\frac{\mathbf{c}}{\mathbf{a}}+\frac{\mathbf{a}}{\mathrm{b}}=1\), then \(\cos (\beta-\gamma)+\cos (\gamma-\alpha)+\cos (\alpha-\beta)\) is equal to

117995 One of the values of \(\left(\frac{1+i}{\sqrt{2}}\right)^{2 / 3}\) is

118000 What is the value of
\(\left(\frac{i+\sqrt{3}}{-i+\sqrt{3}}\right)^{52722}+\left(\frac{i-\sqrt{3}}{i+\sqrt{3}}\right)^{40305} \text { where } i=\sqrt{-1} \text { ? }\)

117993 If \(a=\cos 2 \alpha+i \sin 2 \alpha, b=\cos 2 \beta+i \sin 2 \beta\), \(c=\cos 2 \gamma+i \sin 2 \gamma\) and \(d=\cos 2 \delta+i \sin 2 \delta\), then
\(\sqrt{\text { abcd }}+\frac{1}{\sqrt{\text { abcd }}}=\)

117994 If \(a=\cos \alpha+i \sin \alpha, b=\cos \beta+i \sin \beta\), \(\mathbf{c}=\cos \gamma+i \sin \gamma\) and \(\frac{\mathbf{b}}{\mathbf{c}}+\frac{\mathbf{c}}{\mathbf{a}}+\frac{\mathbf{a}}{\mathrm{b}}=1\), then \(\cos (\beta-\gamma)+\cos (\gamma-\alpha)+\cos (\alpha-\beta)\) is equal to

117995 One of the values of \(\left(\frac{1+i}{\sqrt{2}}\right)^{2 / 3}\) is

118000 What is the value of
\(\left(\frac{i+\sqrt{3}}{-i+\sqrt{3}}\right)^{52722}+\left(\frac{i-\sqrt{3}}{i+\sqrt{3}}\right)^{40305} \text { where } i=\sqrt{-1} \text { ? }\)

117993 If \(a=\cos 2 \alpha+i \sin 2 \alpha, b=\cos 2 \beta+i \sin 2 \beta\), \(c=\cos 2 \gamma+i \sin 2 \gamma\) and \(d=\cos 2 \delta+i \sin 2 \delta\), then
\(\sqrt{\text { abcd }}+\frac{1}{\sqrt{\text { abcd }}}=\)

117994 If \(a=\cos \alpha+i \sin \alpha, b=\cos \beta+i \sin \beta\), \(\mathbf{c}=\cos \gamma+i \sin \gamma\) and \(\frac{\mathbf{b}}{\mathbf{c}}+\frac{\mathbf{c}}{\mathbf{a}}+\frac{\mathbf{a}}{\mathrm{b}}=1\), then \(\cos (\beta-\gamma)+\cos (\gamma-\alpha)+\cos (\alpha-\beta)\) is equal to

117995 One of the values of \(\left(\frac{1+i}{\sqrt{2}}\right)^{2 / 3}\) is