What is 3e^{-j(pi/4)} ?

The solution to 3e^{-j(pi/4)} is 3/(e^{\frac{pij){4}}}

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simplify 3e^{-j(pi/4)}

simplify

3 e^{- j (\frac{π}{4})}

\frac{3}{e ^{\frac{πj}{4}}}

Solution steps

3 e^{- j (\frac{π}{4})}

Apply exponent rule:

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

= 3 \cdot \frac{1}{e ^{\frac{π}{4} j}}

\frac{1}{e ^{j \frac{π}{4}}} = \frac{1}{e ^{\frac{πj}{4}}}

= 3 \cdot \frac{1}{e ^{\frac{πj}{4}}}

Multiply fractions:

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

= \frac{1 \cdot 3}{e ^{\frac{πj}{4}}}

Multiply the numbers:

1 \cdot 3 = 3

= \frac{3}{e ^{\frac{πj}{4}}}

1.5 \cdot 4 \cdot 1 0^{- 4}

- 4 (2.03)^{3} (0.9)^{- 5}

21600 \cdot 1.6 \cdot 1 0^{- 19}