What is the value of cos((2pi)/5)+i*sin((2pi)/5) ?

The value of cos((2pi)/5)+i*sin((2pi)/5) is (sqrt(2)sqrt(3-\sqrt{5)})/4+i(sqrt(2)sqrt(5+\sqrt{5)})/4

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cos((2pi)/5)+i*sin((2pi)/5)

cos (\frac{2 π}{5}) + i \cdot sin (\frac{2 π}{5})

\frac{2 3 - 5}{4} + i \frac{2 5 + 5}{4}

Solution steps

cos (\frac{2 π}{5}) + i sin (\frac{2 π}{5})

Rewrite using trig identities:

cos (\frac{2 π}{5}) = \frac{2 3 - 5}{4}

Rewrite using trig identities:

sin (\frac{2 π}{5}) = \frac{2 5 + 5}{4}

= \frac{2 3 - 5}{4} + i \frac{2 5 + 5}{4}

sec (arccot (\frac{2 21}{21}))

- arcsin (- 1)

arctan (- \frac{3}{8})

sin (arcsin (\frac{7}{25}) + arccos (- \frac{5}{13}))

\frac{12 sin ( 2 8 ^{\circ} )}{sin ( 10 4 ^{\circ} )}

What is the value of cos((2pi)/5)+i*sin((2pi)/5) ?
The value of cos((2pi)/5)+i*sin((2pi)/5) is (sqrt(2)sqrt(3-\sqrt{5)})/4+i(sqrt(2)sqrt(5+\sqrt{5)})/4