What is |e^{i(2t+pi/4)}| ?

The solution to |e^{i(2t+pi/4)}| is sqrt(cos^2((8t+pi)/4)+sin^2((8t+pi)/4))

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simplify |e^{i(2t+pi/4)}|

simplify

e^{i (2 t + \frac{π}{4})}

cos^{2} (\frac{8 t + π}{4}) + sin^{2} (\frac{8 t + π}{4})

Solution steps

e^{i (2 t + \frac{π}{4})}

Apply imaginary number rule:

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

= cos (\frac{8 t + π}{4}) + i sin (\frac{8 t + π}{4})

∣ a + bi ∣ = (a + bi) (a - bi) = a^{2} + b^{2}

With

a = cos (\frac{8 t + π}{4}), b = sin (\frac{8 t + π}{4})

= cos^{2} (\frac{8 t + π}{4}) + sin^{2} (\frac{8 t + π}{4})

(L^{\frac{1}{2}} + K^{\frac{1}{2}})^{2}

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

(- 8 i + (- 5), 2 j) \cdot (9, 7 i + (- 0), 7 j)

- \frac{2 ( 4 + 79 )}{3}

\frac{n ( n - 1 ) ^{2}}{2}

What is |e^{i(2t+pi/4)}| ?
The solution to |e^{i(2t+pi/4)}| is sqrt(cos^2((8t+pi)/4)+sin^2((8t+pi)/4))