If ` z=sintheta-icostheta` then for any integer n,

If z = sin theta -i cos theta then for any integer n,

If A=[[costheta,sintheta],[-sintheta,costheta]] , then for any natural number, find the value of D e t\ (A^n) .

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)

(sintheta+icostheta)^n is equal to

(1+sintheta+icostheta)^(n)

If z = (3+isintheta)/(4-icostheta) is purely real and theta in (pi/2,pi) ,then arg(sintheta + i costheta) is -

If z = (3+isintheta)/(4-icostheta) is purely real and theta in (pi/2,pi) ,then arg(sintheta + i costheta) is -

If frac{3+isintheta}{4-icostheta}, theta in [0,2pi] , is a real number, then an argument of sintheta+icostheta is

If A(theta)=[[sintheta, icostheta], [icostheta, sintheta]] , then which of the following is not true? (a) A(theta)^(-1)=A(pi-theta) (b) A(theta)+A(pi+theta) is a null matrix (c) A(theta)^(-1) is invertible for all theta in R (d) A(theta)^(-1)=A(-theta)