Convert \({\rm{ }}\,2\left( {\cos \left( { - \dfrac{\pi }{4}} \right) + i\sin \left( { - \dfrac{\pi }{4}} \right)} \right){\rm{ }}\) into the cartesian form.

Given that, on the Argand diagram the points A and B represent the complex numbers \({\rm{ }}{z_1} = 2i\) and \({z_2} = \sqrt 3 + i\) respectively, then \(\arg \left( {{z_1} + {z_2}} \right) = \,\,?\)

Convert \(4i\) into the mod-arg form

Convert \(\dfrac{1}{{1 + i}}\) into the mod-arg form

Convert \({\left( {\sqrt 3 + i} \right)}\) into the mod-arg form

Convert \(4\left( {\cos \left( { - \dfrac{{5\pi }}{6}} \right) + i\sin \left( { - \dfrac{{5\pi }}{6}} \right)} \right)\) into the cartesian form.

Convert \(\sqrt 2 \left( {\cos \left( { - \dfrac{\pi }{4}} \right) + i\sin \left( { - \dfrac{\pi }{4}} \right)} \right)\) into the cartesian form

(i) Convert \(2+2i\) into mod-arg form. (3 marks)

(ii) Convert \(5(\cos (\dfrac{\pi }{3}) - i\sin (\dfrac{\pi }{3}))\) into the cartesian form (3 marks)

Express \(2 \text { cis } \dfrac{5\pi}{6}\) in \( x+i y\) form where \( x, y \) are real

Express \(2 \text { cis } \dfrac{\pi}{6}\) in \( x+i y\) form where \( x, y \) are real