What is e^{t/2}*e^{-jk^2t} ?

The solution to e^{t/2}*e^{-jk^2t} is e^{(t-2jtk^2)/2}

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simplify e^{t/2}*e^{-jk^2t}

simplify

e^{\frac{t}{2}} \cdot e^{- j k^{2} t}

e^{\frac{t - 2 j t k ^{2}}{2}}

Solution steps

e^{\frac{t}{2}} e^{- j k^{2} t}

Apply exponent rule:

a^{- b} = \frac{1}{a ^{b}}

= e^{\frac{t}{2}} \frac{1}{e ^{j t k^{2}}}

Multiply fractions:

a \cdot \frac{b}{c} = \frac{a \cdot b}{c}

= \frac{1 \cdot e ^{\frac{t}{2}}}{e ^{j k^{2} t}}

Multiply:

1 \cdot e^{\frac{t}{2}} = e^{\frac{t}{2}}

= \frac{e ^{\frac{t}{2}}}{e ^{j t k^{2}}}

Apply exponent rule:

\frac{x ^{a}}{x ^{b}} = x^{a - b}

\frac{e ^{\frac{t}{2}}}{e ^{j t k^{2}}} = e^{\frac{t}{2} - j t k^{2}} = e^{\frac{t - 2 j t k ^{2}}{2}}

= e^{\frac{t - 2 j t k ^{2}}{2}}

370.85 \cdot (25)^{- 0.9765}

4. 5^{2} \cdot e^{- 4.5}

1.59 \cdot 1 0^{- 10}

\frac{2}{a} π r a d a^{0}

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

What is e^{t/2}*e^{-jk^2t} ?
The solution to e^{t/2}*e^{-jk^2t} is e^{(t-2jtk^2)/2}