What is 1/4 e^{j((5npi)/4)}*e^{-j^2pin} ?

The solution to 1/4 e^{j((5npi)/4)}*e^{-j^2pin} is 1/4 e^{(5pijn)/4-pij^2n}

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simplify 1/4 e^{j((5npi)/4)}*e^{-j^2pin}

simplify

\frac{1}{4} e^{j (\frac{5 nπ}{4})} \cdot e^{- j^{2} πn}

\frac{1}{4} e^{\frac{5 πjn}{4} - π j^{2} n}

Solution steps

\frac{1}{4} e^{j (\frac{5 nπ}{4})} e^{- j^{2} πn}

Apply exponent rule:

a^{b} \cdot a^{c} = a^{b + c}

e^{j \frac{5 nπ}{4}} e^{- j^{2} πn} = e^{j \frac{5 πn}{4} - π j^{2} n}

= \frac{1}{4} e^{j \frac{5 nπ}{4} - j^{2} πn}

Multiply

j \frac{5 nπ}{4} : \frac{5 πjn}{4}

= \frac{1}{4} e^{\frac{5 nπj}{4} - j^{2} πn}

\frac{500}{1 0 ^{9}} \cdot (7.8 \cdot 1 0^{- 9})

θ e^{- θ (l n (z θ) θ)}

e^{- 3 x} e^{3 x}

(\frac{7}{3})^{3}

(3 x y^{2} z^{2}) (15 x^{2} y z^{3})

What is 1/4 e^{j((5npi)/4)}*e^{-j^2pin} ?
The solution to 1/4 e^{j((5npi)/4)}*e^{-j^2pin} is 1/4 e^{(5pijn)/4-pij^2n}