Find the sum of the following geometric series: `a/(1+i)+a/((1+i)^2)+a/((1+i)^3)++a/((1+i)^n)dot`

Find the sum of the following geometric series: 1,\ -a,\ a^2,-a^3,... to\ n terms (a!=1)

Find the modulus of the following complex numbers (1+i)/(1-i) - (1-i)/(1+i)

Find the conjugates of the following complex number: ((3-2i)(2+3i))/((1+2i)(2-i))

Convert the following in the polar form : (i) (1+7i)/((2-i)^2) (ii) (1+3i)/(1-2i)

Find the sum of n terms of the series whose nth terms is (i) n(n-1)(n+1) .

Find the sum of n terms \ of the series: 1/(1. 2)+1/(2. 3)+1/(3. 4)+dot+1/(ndot(n+1))

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

The value of 1+(1+i)+(1+i^2) +(1+i^3) =

Find the values of n and bar X in each of the following cases: (i) sum_(i=1)^n (x_1-12)=-10 and sum_(i=1)^n (x_1-3)=62 (ii) sum_(i=1)^n (x_1-10)=30 and sum_(i=1)^n (x_1-6)=150

Express the following complex number in the polar form: (i) (1+7i)/(2-i)^2 (ii) (1+3i)/(1-2i)