(sin x)/((ii))(1+i)^(4)(1+(1)/(i))^(4)

((1+i)/(1-i))^(4)+((1-i)/(1+i))^(4)=

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 .

((1+i)/(1-i))^4+((1-i)/(1+i))^4=

(1+i)^(4)+(1-i)^(4)=

Simplify the following : (i) [i^(19) +(1)/(i^(25))]^(2) (ii) [i^(5)- (1)/(i^(3))]^(4)

Simplify the following : (i) [i^(19) +(1)/(i^(25))]^(2) (ii) [i^(5)- (1)/(i^(3))]^(4)

If x+(1)/(x)=4; Find ( i ) x^(2)+(1)/(x^(2)) (ii) x^(4)+(1)/(x^(4))

If (x-(1)/(x))=4 , find the value of (i)(x^(2)+(1)/(x^(2))), (ii)(x^(4)+(1)/(x^(4)))

If x + (1)/(x) = 5 find the values of (i) x^(2) + (1)/(x^(2)) and (ii) x^(4) + (1)/(x^(4))