Prove that `(1 - i)^(4) = -4`.

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

Prove that : (1 + i)^(4n) and (1 + i)^(4n + 2) are real and purely imaginary respectively.

Prove that: (i) (1-i)^(2)=-2i (ii) (1+i)^(4)xx(1+(1)/(i))^(4)=16 (iii) {i^(19)+((1)/(i))^(25)}^(2)=-4 (iv) i^(4n)+i^(4n+1)+i^(4n+2)+i^(4n+3)=0 (v) 2i^(2)+6i^(3)+3i^(16)-6i^(19)+4i^(25)=1+4i .

If A = [(4,2),(-1,1)] and I = [(1,0),( 0,1)] prove that (A - 2I) (A - 3I) = 0

Prove that: sec^4A(1-sin^4A) -2 tan^2A=1 .

Prove that (1+i)^4(1+1/i)^4=16

Prove that 1+i^2+i^4+i^6 =0

If A=[[4, 2],[-1, 1]] , prove that (A-2I)(A-3I)=O .

Prove that (1+i)^4 x (1+frac{1}{i})^4 = 16

prove that sec^4 A(1-sin^4 A) - 2tan^2 A = 1.