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))# ?

1 Answer
Hriman
Jul 6, 2018

#-(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#

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