What is 5e^{(pii)/4} ?

The solution to 5e^{(pii)/4} is 5/(2^{1/2)}+i 5/(2^{1/2)}

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simplify 5e^{(pii)/4}

simplify

5 e^{\frac{πi}{4}}

\frac{5}{2 ^{\frac{1}{2}}} + i \frac{5}{2 ^{\frac{1}{2}}}

Solution steps

5 e^{\frac{πi}{4}}

e^{\frac{πi}{4}} = \frac{1 + i}{2 ^{\frac{1}{2}}}

= 5 \cdot \frac{1 + i}{2 ^{\frac{1}{2}}}

Multiply fractions:

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

= \frac{( 1 + i ) \cdot 5}{2 ^{\frac{1}{2}}}

Rewrite

\frac{( 1 + i ) \cdot 5}{2 ^{\frac{1}{2}}}

in standard complex form:

\frac{5}{2 ^{\frac{1}{2}}} + \frac{5}{2 ^{\frac{1}{2}}} i

= \frac{5}{2 ^{\frac{1}{2}}} + \frac{5}{2 ^{\frac{1}{2}}} i

(3 x + 1) 2

\frac{( - 72 )}{( - 9 )}

\frac{x ^{4}}{2 x ^{4}}

\frac{2}{5} - \frac{4}{17}

(\frac{3 ^{2}}{6})^{2}

What is 5e^{(pii)/4} ?
The solution to 5e^{(pii)/4} is 5/(2^{1/2)}+i 5/(2^{1/2)}