2 squareroot 2cos 7 pi7 1 sm 7 pi45 cos 290 degree 1 sm 29

[2 squareroot 2(cos 7 pi/7 + 1 sm 7 pi/4)]^5 cos 290 degree + 1 sm 290 degree)^10 [10(cos 3 pi/4 + 1 sm 3 pi/s)]^3

Solution

[22((cos(7_/4)+isin(7_/4))]⁵

=(22)⁵((cos(5*7_/4)+isin(5*7_/4))

=(1282)((cos(35_/4)+isin(35_/4))

=(1282)((cos(8 +3_/4)+isin(8 +3_/4))

=(1282)((cos(3_/4)+isin(3_/4))

=(1282)((-1_/2)+i(1_/2))

=(128 +i128)

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(cos240^o+isin240^o)¹⁰

=(cos(10*240^o)+isin(10*240^o))

=(cos(2400^o)+isin(2400^o))

=(cos(2160+240)^o+isin(2160+240)^o))

=(cos(2160+240)^o+isin(2160+240)^o))

=(cos(240)^o+isin(240)^o))

=(-1_/2)+i(-(3)_/2)

=-(1_/2)-i((3)_/2)

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[10(cos(3_/4)+isin(3_/4))]³

=[(10³)(cos(3*3_/4)+isin(3*3_/4))]

=[(10³)(cos(9_/4)+isin(9_/4))]

=[(10³)(cos(2 +_/4)+isin(2 +_/4))]

=[(10³)(cos(_/4)+isin(_/4))]

=[(1000)((1_/2)+i(1_/2))]

=[5002+ i5002]