What is (sin(θ)-icos(θ))^2 ?

The solution to (sin(θ)-icos(θ))^2 is -cos(2θ)-sin(2θ)i

Popular >

simplify (sin(θ)-icos(θ))^2

simplify

(sin (θ) - i cos (θ))^{2}

- cos (2 θ) - sin (2 θ) i

Solution steps

(sin (θ) - i cos (θ))^{2}

Apply Perfect Square Formula:

(a - b)^{2} = a^{2} - 2 ab + b^{2}

(sin (θ) - i cos (θ))^{2} = sin^{2} (θ) - 2 sin (θ) i cos (θ) + (i cos (θ))^{2}

= sin^{2} (θ) - 2 sin (θ) i cos (θ) + (i cos (θ))^{2}

Simplify

sin^{2} (θ) - 2 sin (θ) i cos (θ) + (i cos (θ))^{2} : - i sin (2 θ) - cos (2 θ)

= - i sin (2 θ) - cos (2 θ)

Rewrite in standard complex form:

- cos (2 θ) - sin (2 θ) i

= - cos (2 θ) - sin (2 θ) i

(x - 1 - a)^{2}

(e^{5 x} + e^{7 x}) (e^{8 x} - e^{- x})

- \frac{1}{s ( s + 5 )}

(x - 1 + 2)^{2}

(0.34 arcsin (\frac{- x + 3.14}{1.35}) + 2.38)^{2}

What is (sin(θ)-icos(θ))^2 ?
The solution to (sin(θ)-icos(θ))^2 is -cos(2θ)-sin(2θ)i