(sqrt(12))*{i^(19)+((1)/(dot i))^(25)}^(2)=-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 .

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

(1)/(4)xx sqrt ([(12.1)^(2)-(8.1)^(2)] div [(0.25)^(2)+(0.25)(19.95)]) .

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)

sqrt([(12.1)^(2)-(8.1)^(2)]-:[(0.25)^(2)+(0.25)(19.95)])

For the system of equations given by x^(5)+y^(5)=33 and x+y=3, the possible ordered pair(s) of (x,y) can be (A) ((3)/(2)+(sqrt(17))/(2)i,(3)/(2)-(sqrt(17))/(2)i)(B)(3)/(2)+(sqrt(19))/(2)i,(3)/(2)-(sqrt(19))/(2)i)(C)(3)/(2)+(sqrt(19))/(2)i,(3)/(2)-(sqrt(19))/(2)i)(D)(3)/(2)-(sqrt(19))/(2)i,(3)/(2)+(sqrt(19))/(2)i])

If z=sqrt(3)-2+i , then principal value of argument z is (where i=sqrt(-1) (1) -(5pi)/(12) (2) pi/(12) (3) (7pi)/(12) (4) (5pi)/(12)