(1-i)^(4)quad " c."(-2-(1)/(3)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)

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

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

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 .

If i=sqrt(-)1, then 4+5(-(1)/(2)+(i sqrt(3))/(2))^(334)+3(-(1)/(2)+(i sqrt(3))/(2))^(365) is equal to (1)1-i sqrt(3)(2)-1+i sqrt(3)(3)i sqrt(3)(4)-i sqrt(3)

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

Simplify : {:((i),3(6+6i)+i(6+6i),(ii),(1-i)-(-3+6i)),((iii),((1)/(3)-(2)/(3)i)-(4+(3)/(2)i),(iv),{((1)/(5)+(7)/(5)i)-(6+(1)/(5)i)}-((-4)/(5)+i)):}

(Acitity) Express (1)/(i^(1)) + (2)/( i ^(2)) +(3)/( i ^(3)) + (5)/( i ^(4)) in the form of (a + ib).