What is 1+3e^{i-3/2 pi} ?

The solution to 1+3e^{i-3/2 pi} is (e^{(3pi)/2}+3cos(1))/(e^{(3pi)/2)}+i(3sin(1)}{e^{\frac{3pi)/2}}

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simplify 1+3e^{i-3/2 pi}

simplify

1 + 3 e^{i - \frac{3}{2} π}

\frac{e ^{\frac{3 π}{2}} + 3 cos ( 1 )}{e ^{\frac{3 π}{2}}} + i \frac{3 sin ( 1 )}{e ^{\frac{3 π}{2}}}

Solution steps

1 + 3 e^{i - \frac{3}{2} π}

3 e^{i - \frac{3}{2} π} = \frac{3}{e ^{\frac{3 π}{2}}} (cos (1) + i sin (1))

= 1 + \frac{3}{e ^{\frac{3 π}{2}}} (cos (1) + i sin (1))

Rewrite

1 + (cos (1) + sin (1) i) \frac{3}{e ^{\frac{3 π}{2}}}

in standard complex form:

\frac{e ^{\frac{3 π}{2}} + 3 cos ( 1 )}{e ^{\frac{3 π}{2}}} + \frac{3 sin ( 1 )}{e ^{\frac{3 π}{2}}} i

= \frac{e ^{\frac{3 π}{2}} + 3 cos ( 1 )}{e ^{\frac{3 π}{2}}} + \frac{3 sin ( 1 )}{e ^{\frac{3 π}{2}}} i

\frac{1}{5 + i}

\frac{18 x ^{7} y ^{5}}{30 x y ^{4}}

2 x - 2 x

\frac{a ^{2} + 2 ab}{a + b} + \frac{b ^{2}}{a + b}

What is 1+3e^{i-3/2 pi} ?
The solution to 1+3e^{i-3/2 pi} is (e^{(3pi)/2}+3cos(1))/(e^{(3pi)/2)}+i(3sin(1)}{e^{\frac{3pi)/2}}