Let `z_(1)= cos 12^(@) + I sin 12^(@) and z_(2) = cos 48^(@) + i. sin 48^(@)`. Write complex number `(z_(1) + z_(2))` in polar form. Find its modulus and argument.

Explanation

`z_(1) + z_(2) = cos 12^(@) + cos 48^(@) = I (sin 48^(@) + sin 12^(@))`
`= 2cos 30^(@)-cos 18^(@) + 2i sin 30^(@) . Cos 18^(@)`
`=2 cos 18^(@) ( cos 30^(@) + I sin 30^(@))`
`therefore |z| = 2 cos 18^(@)`
and `arg(z) = 30^(@)`