Express `1/(1-costheta+2isintheta)` in the form `x+i y` .

Express (1)/(1-i) in the form a+ib .

choose the correct pair of statement : (i) (costheta+isintheta)^(n)=cosntheta+isinntheta , x is an integer (ii) (sintheta+icostheta)^(n)=sinntheta+icosthetantheta , n is an integer (iii) If z=costheta+isintheta , then z^(-1)=costheta-isintheta (iv)(z+barz)/(2)=Re(z)

If x=(2sintheta)/(1+costheta+sintheta),t h e n(1-costheta+sintheta)/(1+sintheta) is equal to 1+x (b) 1-x (c) x (d) 1/x

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

Express each of the following equations in the form of ax + by + c = 0 and write the values of a, b and c. (i) 3x + 4y = 5 (ii) x - 5 = sqrt3y (iii) 3x = y (iv) x/2+y/2=1/6 (v) 3x - 7 = 0

Consider the differential equation (dy)/(dx)=e^(x-y+)x^(2)e^(-y) i . Express the equation in the form f(x)dx=g(y)dy. ii . Hence solve the equation.

If (costheta +isintheta)(cos2theta +isin2theta).....(cosntheta + isinntheta) = 1 then the value of theta is:

Consider the integral I=int(xe^(x))/((1+x)^(2))dx Express the integral I in the form inte^(x)(f(x)+f'(x))dx

Consider the lines (x-3)/3=(y-8)/(-1)=(z-3)/1 and (x+3)/(-3) =(y+7)/2=(z-6)/4 i.Express the equations in the vector form. ii. Find the shortest distance between these lines.

If x+iy = (3)/(2+costheta+ isintheta) prove that x^(2)+y^(2)=4x-3