Question

Write the number given in polar form in the form of a + ib a. `z= 5(cos(7pi/6) +isin(7pi/6)` b. `z= 6(cos (pi/8) +isin(pi/8))` ?

Answer 1

`-(5sqrt3)/2-5/2i`

`3sqrt(2+sqrt2)+3sqrt(2+sqrt2)i`

Explanation:

Write the number given in polar form in the form of a + ib
a. `z= 5(cos(7pi/6) +isin(7pi/6))`
b. `z= 6(cos (pi/8) +isin(pi/8))`

Distribute:
`a. 5cos((7pi)/6)+5isin((7pi)/6)=5*-sqrt3/2*5+5*-1/2i=`
`-(5sqrt3)/2-5/2i`

b. `z= 6(cos (pi/8) +isin(pi/8))=6*(sqrt(2+sqrt2))/2+6*(sqrt(2+sqrt2))/2i=3sqrt(2+sqrt2)+3sqrt(2+sqrt2)i`