What is the value of 4(cos((7pi)/4)+isin((7pi)/4)) ?

The value of 4(cos((7pi)/4)+isin((7pi)/4)) is 2sqrt(2)-2sqrt(2)i

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4(cos((7pi)/4)+isin((7pi)/4))

4 (cos (\frac{7 π}{4}) + i sin (\frac{7 π}{4}))

22 - 22 i

Solution steps

4 (cos (\frac{7 π}{4}) + i sin (\frac{7 π}{4}))

Rewrite using trig identities:

cos (\frac{7 π}{4}) = \frac{2}{2}

Rewrite using trig identities:

sin (\frac{7 π}{4}) = - \frac{2}{2}

= 4 (\frac{2}{2} + i (- \frac{2}{2}))

Simplify

4 (\frac{2}{2} + i (- \frac{2}{2})) : 22 - 22 i

= 22 - 22 i

cos (5 π) + i sin (5 π)

\frac{sin ( 15 0 ^{\circ} ) + cot ( 31 5 ^{\circ} )}{3 cos ( 21 0 ^{\circ} )}

0.23 \cdot sin (62. 2^{\circ})

tan (\frac{3 π}{16})

19.6 cos (3 0^{\circ})

What is the value of 4(cos((7pi)/4)+isin((7pi)/4)) ?
The value of 4(cos((7pi)/4)+isin((7pi)/4)) is 2sqrt(2)-2sqrt(2)i