Modulus of `(cos theta-isin theta)/(sin theta-icos theta)` is

((cos theta+isin theta)^4)/((sin theta+icos theta)^5)=?

((cos3theta-isin3theta)^4)/((sin2theta+icos2theta)^5)=

Express the following in a + ib form: (i) ((cos theta+ isin theta)/(sin theta + icos theta))^(4) (ii) ((cos 2theta -isin2theta)^(4)(cos4theta +isin4theta)^(-5))/((cos 3theta +isin3theta)^(-2) (cos 3theta -isin 3theta)^(-9)) (iii) ((sinpi//8 +icos pi//8)^(8))/((sinpi//8-icospi//8)^(8))

Express the following in a + ib form: (i) ((cos theta+ isin theta)/(sin theta + icos theta))^(4) (ii) ((cos 2theta -isin2theta)^(4)(cos4theta +isin4theta)^(-5))/((cos 3theta +isin3theta)^(-2) (cos 3theta -isin 3theta)^(-9)) (iii) ((sinpi//8 +icos pi//8)^(8))/((sinpi//8-icospi//8)^(8))

Evaluate the following determinants: (b) |(cos theta, -sin theta),(sin theta, cos theta)| = cos theta (cos theta) - sin theta(-sin theta) = cos^(2) theta + sin^(2) theta = 1

Find the characteristic roots of the two-rowed orthogonal matrix [(cos theta,-sin theta),(sin theta,cos theta)] and verify that they are of unit modulus.

Find the characteristic roots of the two-rowed orthogonal matrix [(cos theta,-sin theta),(sin theta,cos theta)] and verify that they are of unit modulus.

Find the characteristic roots of the two-rowed orthogonal matrix [(cos theta,-sin theta),(sin theta,cos theta)] and verify that they are of unit modulus.

Find the characteristic roots of the two-rowed orthogonal matrix [(cos theta,-sin theta),(sin theta,cos theta)] and verify that they are of unit modulus.