निम्नलिखित को सरल बनाएं:(i) [i^(19) +(1)/(i^(25))]^(2) (ii) [i^(5)- (1)/(i^(3) )]^(4) | कक्षा 11...

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

Evaluate: [i^(19)+((1)/(i))^(25)]^(2)

(v) (1-i) ^ (2) (1 + i) - (3-4i) ^ (2)

Evaluate: " "(i)" "i^(19)" "(ii)" "i^(62)" "(iii)" "i^(373)

. (i) i= 2 A (ii) i_1 = (10)/(3) A (iii) i_2 = - (4)/(3) A .

Show that: {i^(19)+((1)/(i))^(25)}^(2)=-4( ii) {i^(17)-((1)/(i))^(34)}^(2)=2i (iii) {i^(18)+((1)/(i))^(24)}^(3)=0 (iv) i^(n)+i^(n+1)+i^(n+2)+i^(n+3)=0 for all n in N.

Evaluate: (i^(2)+i^(4)+i^(6)+i^(7))/(1+i^(2)+i^(3))

The value of (1+i) (1-i^(2)) (1+i^(4))(1-i^(5)) is

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 .

Find the values of the following : (i) i^(7)+i^(17)+i^(12) (ii) i^(11)+i^(-11) (iii) i^(3)+(1)/(i^(3)) (iv) 1+i^(2)+i^(6)+i^(8)