N 23
we have

Remember that

substitute given values
![s\imaginaryI n((3pi)/(4)+(5pi)/(6))=s\imaginaryI n((3p\imaginaryI)/(4))cos((5p\imaginaryI)/(6))+cos((3p\imaginaryI)/(4)\operatorname{\lparen}s\imaginaryI n((5p\imaginaryI)/(6))]()
Remember that
3pi/4=135 degrees ------> reference angle is 45 degrees
135 degrees -----> II quadrant ----> sine is positive and cosine is negative
so
sin(3pi/4)=sin(45)=√2/2
cos(3pi/4)=-cos(45)=-√2/2
5pi/6=150 degrees ----> reference angle is 30 degrees
150 degrees -----> II quadrant -----> sine is positive and cosine is negative
sin(5pi/6)=sin(30)=1/2
cos(5pi/6)=-cos(30)=-√3/2
Substitute the given values in the formula


The answer is
