What is (1-e^{i*θ})^2 ?

The solution to (1-e^{i*θ})^2 is (1-cos(θ)-isin(θ))^2

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simplify (1-e^{i*θ})^2

simplify

(1 - e^{i \cdot θ})^{2}

(1 - cos (θ) - i sin (θ))^{2}

Solution steps

(1 - e^{i θ})^{2}

Apply imaginary number rule:

e^{ia} = cos (a) + i sin (a)

= (1 - (cos (θ) + i sin (θ)))^{2}

Expand

1 - (cos (θ) + sin (θ) i) : 1 - cos (θ) - sin (θ) i

= (1 - cos (θ) - i sin (θ))^{2}

- 3 (- 3 csc^{3} (x) cot^{2} (x) - csc^{5} (x))

(n^{2} + n - 1 - kn) (n^{2} + n - 1 + kn)

(x + \frac{1}{2}) (x - 5)

\frac{d ^{2} y}{d ^{2} x} (x + x y + y = 1)

(x + \frac{1}{2}) (x - 1)