If `z=(1-i sin theta)/(1-icos theta)` is a real number,then the value of |z| is (where `i=sqrt(-1)`)

If pi < theta < 2pi and z=1+cos theta + i sin theta , then write the value of |z|

Using De Moivre 's theorem prove that : ((1+cos theta +i sin theta)/(1+cos theta - i sin theta))^n= cos n theta + i sin n theta , where i = sqrt(-1)

If z=(1+i)/sqrt2 , then the value of z^1929 is

Consider the complex number z = (1 - isin theta)//(1+ icos theta) . The value of theta for which z is purely real are

If (cos^(3) theta )/( (1- sin theta ))+( sin^(3) theta )/( (1+ cos theta ))=1+ cos theta , then number of possible values of theta is ( where theta in [0,2pi] )

Consider the complex number z = (1 - isin theta)//(1+ icos theta) . The value of theta for which z is purely imaginary are

Consider the complex number z = (1 - isin theta)//(1+ icos theta) . The value of theta for which z is unimodular give by

If a = cos theta +theta i sin, "then find the value of" (1+a)/(1-a) .

Consider the complex number z = (1 - isin theta)/(1+ icos theta) . If agrument of z is pi/4 , then (a) theta = npi, n in I only (b) theta= (2n + 1), n in I only (c) both theta= npi and theta = (2n + 1)(pi)/(2), n in I (d) none of these

If sin^(3) theta+sin theta cos theta+ cos^(3) theta=1 , then theta is equal to (n in Z)