What is (e^{ix}-cos(x))^2 ?

The solution to (e^{ix}-cos(x))^2 is -sin^2(x)

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simplify (e^{ix}-cos(x))^2

simplify

(e^{i x} - cos (x))^{2}

- sin^{2} (x)

Solution steps

(e^{i x} - cos (x))^{2}

Apply imaginary number rule:

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

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

Simplify

cos (x) + sin (x) i - cos (x) : i sin (x)

= (i sin (x))^{2}

Apply exponent rule:

(a \cdot b)^{n} = a^{n} b^{n}

= i^{2} sin^{2} (x)

i^{2} = - 1

= - 1 \cdot sin^{2} (x)

Multiply:

1 \cdot sin^{2} (x) = sin^{2} (x)

= - sin^{2} (x)

\frac{2 x ^{3} - x + 4}{x + 1} + x^{2}

(1 + b e) (1 + a d)

(2 π + j w) (- j w - 2 π)

\frac{( 5 - 2 m ^{5} ) ^{2}}{25}

x^{2} (x^{3} + 5 x^{2} - 3 x + 3)