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

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

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

simplify

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

- sin^{2} (x)

Solution steps

(e^{x i} - 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{6}{7} - x)^{5}

\frac{\partial}{\partial x} ((x) (x - 3) (y - 4))

f (x) x (2 (y)^{''} - x (y)^{'} = e^{- x})

e^{x} (x + e^{x})

\frac{x ( 2 - x ) ^{4}}{4}