{i^(21)-((1)/(i))^(46)}^(2)=2i

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 .

(-i)(2i)(-(1)/(8)i)^(3)

If I_(1)=int_(x)^(1)(1)/(1+t^(2))dt and I_(2)=int_(1)^((1)/(2))(1)/(1+t^(2))dt for x>=0 then (A) I_(1)=I_(2)(B)I_(1)>I_(2)(C)I_(1)

(1+2i)/(1-(1-i)^2)

Prove that the matrix A=[[(1+i)/(2),(-1+i)/(2)(1+i)/(2),(1-i)/(2)]] is

Express each of the following in the form (a + ib) and find its conjugate: {:((i),(1)/((4+3i)),(ii),(2+3i)^(2),(iii),((2-i))/((1-2i)^(2))),((iv),((1+i)(1+2i))/((1+3i)),(v),((1+2i)/(2+i))^(2),(vi),((2+i))/((3-i)(1+2i))):}

Given that, z=(1+2i)/(1-i)=((1+2i)(1+i))/((1-i)(1+i))

If sum_(i=1)^(7) i^(2)x_(i) = 1 and sum_(i=1)^(7)(i+1)^(2) x_(i) = 12 and sum_(i=1)^(7)(i+2)^(2)x_(i) = 123 then find the value of sum_(i=1)^(7)(i+3)^(2)x_(i)"____"

If sum_(i=1)^(7) i^(2)x_(i) = 1 and sum_(i=1)^(7)(i+1)^(2) x_(i) = 12 and sum_(i=1)^(7)(i+2)^(2)x_(i) = 123 then find the value of sum_(i=1)^(7)(i+3)^(2)x_(i)"____"

Reduce ((1)/(1+2i)+(3)/(1-i))((3-2i)/(1+3i)) to the form (a + ib).