(0.1i){6^(-1)+((3)/(2))^(-1)}^(-1)

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 transpose of each of the following matrices : (i) [{:(5),((1)/(2)),(-1):}] (ii) [{:(1,-1),(2,3):}] (iii) [{:(-1,5,6),(sqrt(3),5,6),(2,3,-1):}]

((-1+i sqrt(3))/(2))^(6)+((-1-i sqrt(3))/(2))^(6)+((-1+i sqrt(3))/(2))^(5)+((-1-i sqrt(3))/(2))^(6)

Convert the following in the form of (a+ib) : (i) (1+i)^(4) (ii) (-3+(1)/(2)i)^(3) (iii) (1-i)(3+4i) (iv) (1+i)(1+ 2i)(1+ 3i) (v) (3+5i)/(6-i) (vi) ((2+3i)^(2))/(2+i) (vii) ((1+ i)(2+i))/((3+i)) (viii) (2-i)^(-3)

Convert the following in the form of (a+ib) : (i) (1+i)^(4) (ii) (-3+(1)/(2)i)^(3) (iii) (1-i)(3+4i) (iv) (1+i)(1+ 2i)(1+ 3i) (v) (3+5i)/(6-i) (vi) ((2+3i)^(2))/(2+i) (vii) ((1+ i)(2+i))/((3+i)) (viii) (2-i)^(-3)

((1)/(2)+sqrt(3)/(2)i)^(6)

Find the transpose of each of the following matrices: (i)[(5),((1)/(2)),(-1)] (ii) [(1,-1),(2,3)] (iii) [(-1,5,6),(sqrt(3),5,6),(2,3,-1)]

Find the transpose of each of the following matrices: (i)[(5),((1)/(2)),(-1)] (ii) [(1,-1),(2,3)] (iii) [(-1,5,6),(sqrt(3),5,6),(2,3,-1)]