Covert the complex number `z = 1 + cos (8pi)/(5) + i. sin (8pi)/(5)` in polar form. Find its modulus and argument.

Explanation

`z = 1 + cos (8pi)/(5) + I sin (8pi)/(5)`
`= 2cos^(2)(4pi)/(5) + cos .(4pi)/(5)`
`= 2cos.(4pi)/(5)(cos.(4pi)/(5) + isin .(4pi)/(5))`
`= - 2cos.(pi)/(5)(-cos.(pi)/(5) + isin .(pi)/(5))`
`= 2 cos.(pi)/(5)(cos.(pi)/(5)- isin .(pi)/(5))`
`= 2cos.(pi)/(5) (cos(-(pi)/(5)) + isin (-(pi)/(5)))`
Thus, `|z| = 2 cos .(pi)/(5) and arg(z) = (pi)/(5)`