सरल कीजिए :
`(a) (1+2i)-(2-3i)` `(b) (3+2i)(2-4i)`
`(c ) (1+i)^(2)+(1-i)^(2)` `(d) (1)/(i)-(1)/(i^(2))+(1)/(i^(3))-(1)/(i^(4))`

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

(1)/(1-2i)+(3)/(1+4i)

Simplify : (1+i^(3))(1+(1)/(i))^(2)(i^(4)+(1)/(i^(4)))

Convert each of the following in the form of (a + i b) : (i) 3(1+i)-2(2+3i) (ii) (1)/(4-5i) (iii) (1-2i)^(-2) (iv) (2-3i)/(3+5i) (v) [(1)/(1-2i)+(3)/(1+i)][(3+4i)/(2-4i)]

((1+i)/(1-i))^(4)+((1-i)/(1+i))^(4)=(A)1(B)2(C)3(D)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 .

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)

Show that (1+ 2i)/(3+4i) xx (1-2i)/(3-4i) is real