[" 10.Prove that "],[qquad quad (1+i)^(n)+(1-i)^(n)=2^((n)/(2)+1)*cos(n pi)/(4)]

Prove that (1 + i)^(n) + (1 - i)^(n) = 2^((n + 2)/(2)) cos (n pi)/(4)

Prove that (a)(1+i)^(n)+(1-i)^(n)=2^((n+2)/(2))*cos((n pi)/(4)) where n is a positive integer. (b) (1+i sqrt(3))^(n)+(1-i sqrt(3)^(n)=2^(n+1)cos((n pi)/(3)), where n is a positive integer

If n is a positive integer, show that (1 + i)^(n) + (1 - i)^(n) = 2 ^((n+2)/2) cos ((npi)/4) .

If n is a positive integer prove that (1+i)^(2n)+(1-i)^(2n)=2^(n+1)cos((n pi)/(2))

" *.i).i) If "n" is an integer then show that "(1+i)^(2n)+(1-i)^(2n)=2^(n+1)cos(n pi)/(2)

A : (1+i)^(6)+(1-i)^(6)=0 R : If n is a positive integer then (1+i)^(n)+(1-i)^(n)=2^((n//2)+1).cos""(npi)/(4)

1 + i^(2n) + i^(4n) + i^(6n)

Prove that (a) (1+i)^n+(1-i)^n=2^((n+2)/2).cos((npi)/4) , where n is a positive integer. (b) (1+isqrt(3))^n+(1-isqrt(3)^n=2^(n+1)cos((npi)/3) , where n is a positive integer

sum_(n=1)^(20)[sin((2n pi)/(21))-i cos((2n pi)/(21))]=

For a positive integer n show that (1+i)^n+(1-i)^n=2^((n+2)/2) "cos((npi)/4)