`a+i b :1/((2+i)^2)-1/((2-i)^2)`

Express the following in the standard form a+i b :((3-2i)(2+3i))/((1+2i)(2-i))

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

If a+i b=((x+i)^2)/(2x+1) , prove that a^2+b^2=((x+i)^2)/((2x+1)^2)

The value of (i^(5)+i^(6)+i^(7)+i^(8)+i^(9))/(1+i) is (1)/(2)(1+i)(b)(1)/(2)(1-i)(c)1(d)(1)/(2)

Express the following in the standard form a+i b :(1/(1-2i)+3/(1+i))((3+4i)/(2-4i))

(a) Express (1+7i)/((2-i)^(2)) in the form a+ib. (b) Reduce (1)/(1-4i)-(2)/(1+i) in the form a+ib.

If A_i= [ [a^i, b^i] , [b^i, a^i]] and if |a|<1, |b|<1 then sum_(i=1)^oo det(A_i) = (A) a^2/(1-a)^2- b^2/(1-b)^2 (B) a^2/(1-a)^2+ b^2/(1-b)^2 (C) a^2/(1+a)^2- b^2/(1+b)^2 (D) (a^2-b^2)/[(1-a^2)(1-b^2)]

The reflection of the complex number (2-i)/(3+i) (where i=sqrt(-1) in the straight line z(1+i)=bar(z)(i-1) is (-1-i)/(2) (b) (-1+i)/(2)(i(i+1))/(2) (d) (-1)/(1+i)

Simplify : (1+2i)/(1-2i)-(1-2i)/(1+2i)