What is the value of (2(cos((3pi)/4)+isin((3pi)/4)))^3 ?

The value of (2(cos((3pi)/4)+isin((3pi)/4)))^3 is 4sqrt(2)i+4sqrt(2)

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(2(cos((3pi)/4)+isin((3pi)/4)))^3

(2 (cos (\frac{3 π}{4}) + i sin (\frac{3 π}{4})))^{3}

42 i + 42

Solution steps

(2 (cos (\frac{3 π}{4}) + i sin (\frac{3 π}{4})))^{3}

Use the following trivial identity:

cos (\frac{3 π}{4}) = - \frac{2}{2}

Use the following trivial identity:

sin (\frac{3 π}{4}) = \frac{2}{2}

= (2 (- \frac{2}{2} + i \frac{2}{2}))^{3}

Simplify

(2 (- \frac{2}{2} + i \frac{2}{2}))^{3} : 42 i + 42

= 42 i + 42

cos (4 5^{\circ}) 8

cos (23 4^{\circ})

sin (4) (\frac{π}{6})

- csc^{2} (π)

cos (\frac{3 π}{4}) - i sin (\frac{3 π}{4})

What is the value of (2(cos((3pi)/4)+isin((3pi)/4)))^3 ?
The value of (2(cos((3pi)/4)+isin((3pi)/4)))^3 is 4sqrt(2)i+4sqrt(2)