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*Use identity sinxcosx = 1/2sin2x

=5/2sin2x + 5cosx

*then use simple integration gives

=(-5/2 x1/2)cosx + 5sinx + c

= =5/4cosx +5sinx + c

Multiply by complex conjugate

z = 50 / (3+4i) * (3-4i) / (3-4i)

Rationalise

z = 50 ( 3 - 4i) / 25 = 6 - 8i.

5 + 5√ 2 - √ 8 - √ 16    (Break up all terms in terms of square roots of 2)

5 + 5√ 2 - √ 8 - 4

5 + 5√ 2 - 2 √ 2 - 4 

1 + 3√2