What is (cos(θ)-isin(θ))^2 ?

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

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simplify (cos(θ)-isin(θ))^2

simplify

(cos (θ) - i sin (θ))^{2}

cos (2 θ) - sin (2 θ) i

Solution steps

(cos (θ) - i sin (θ))^{2}

Apply Perfect Square Formula:

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

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

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

Simplify

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

= cos (2 θ) - i sin (2 θ)

Rewrite in standard complex form:

cos (2 θ) - sin (2 θ) i

= cos (2 θ) - sin (2 θ) i

1000 (1 + \frac{i}{12})^{12}

ln (x) (\frac{x ^{3}}{3} + 3 x) - \frac{1}{3} (\frac{x ^{3}}{3} + 9 x) + c

(1 - 3 i)^{16}

lo g_{10} (x^{7} y^{- 4})

(b - x + ((x + b) \cdot (5 \cdot b - 3 \cdot x)))^{2}

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