I have the teachers\' solution manual to a textbook, but I don\'t understand how

Question

I have the teachers' solution manual to a textbook, but I don't understand how the signs in the second step were determined

I circiled in yellow the parts that I don't understand. Please explain why the signs do not appear to match with the given calues.

Complex numbers z1 and z2 are given by z, = 2/-60 degree, z2 = 5/45 degree. Determine in polar form: Z1 (z2 - z1 )* = 2e-j60 (5ej45 degree - 2e-j60 degree)* = 2e-j60 degree [(5cos45 degree -2cos60 degree) + y(5sin45 degree + 2sin60 degree)]* = 2e-j60 degree [2.54+j5.27]* = 2e-j60 degree [2.54 -j5.27] = 2e-j60 degree middot 5.85e-j64.27 degree = 11.7e-j124.27 degree. z*2/z1+z2=5e-j45 degree /2e-j60 degree + 5eJ45 degree 5e-J*5 degree/(2 cos 60 degree + 5 cos 45 degree) + j(5 cos 45 degree - 2 sin 60 degree) =5e-j45 degree /4.54+j1.80 = 5e-j45 degree /4.89e-j21-63 degree = 1.02e-j(45 degree +21-63 degree) = 1.02e-J66-63 degree.

Explanation / Answer

you know the formula e^(i*t) = cos(t) + i sin(t)

here, 5 * e^(j45) - 2 e^(-j60)

= 5*(cos(45) + jsin(45)) - 2*(cos(-60) + j sin(-60))

as cos(-t) = cos(t)

= 5 cos(45) - 2cos(60) + j(5sin(45)+2sin(60))

similarly the second one also,

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