i=sqrt(-1)

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Prove that : (i) sqrt(i)= (1+i)/(sqrt(2)) (ii) sqrt(-i)=(1- i)/(sqrt(2)) (iii) sqrt(i)+sqrt(-i)=sqrt(2)

the value of ((1+i sqrt(3))/(1-i sqrt(3)))^(6)+((1-i sqrt(3))/(1+i sqrt(3)))^(6) is

The value of ((1+i sqrt(3))/(1-i sqrt(3)))^(6)+((1-i sqrt(3))/(1+i sqrt(3)))^(6)=

log((1+i sqrt(3))/(1-i sqrt(3)))

The argument of (1-i sqrt(3))/(1+i sqrt(3))=

((-1+i sqrt(3))^(15))/((1-i)^(20))+((-1-i sqrt(3))^(15))/((1+i)^(20)) is

(1+i sqrt(3))^(5)+(1-i sqrt(3))^(5)=

((-1+i sqrt(3))/(2))^(6)+((-1-i sqrt(3))/(2))^(6)+((-1+i sqrt(3))/(2))^(5)+((-1-i sqrt(3))/(2))^(6)