Home
Class 11
MATHS
Prove that (a) (1+i)^n+(1-i)^n=2^((n+2)/...

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

Promotional Banner

Similar Questions

Explore conceptually related problems

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

Prove that 2^n >1+nsqrt(2^(n-1)),AAn >2 where n is a positive integer.

Prove that sum_(k=1)^(n-1)(n-k)cos(2kpi)/n=-n/2 , where ngeq3 is an integer

Show that int_0^(npi+v)|sinx|dx=2n+1-cosv , where n is a positive integer and , 0<=vltpi

Prove that n C_0+^n C_3+^n C_6+=1/3(2^n+2cos(npi)/3) .

If n is a positive integer, prove that |I m(z^n)|lt=n|Im(z)||z|^(n-1.)

The smallest positive integer 'n' for which ((1+i)/(1-i))^(n)=1 is

Find the least positive integer n such that ((1 + i)/(1 - i))^(n) = 1 .

Find the least positive integer n such that ((1+i)/(1-i))^(n)=1 .

if f(x)=(a-x^n)^(1/n), where a > 0 and n is a positive integer, then f(f(x))= (i) x^3 (ii) x^2 (iii) x (iv) -x