lf x+iy13=a+ib then xa+yb=?
a2-b2
2(a2-b2)
3(a2-b2)
4(a2-b2)
Explanation for the correct option:
Step 1: Simplify the term x+iy13=a+ib:
Given: x+iy13=a+ib
x+iy13=a+ibx+iy=a+ib3x+iy=a3+(ib)3+3a2ib+3ab2i2(x+iy)=a3-ib3+i3a2b-3ab2(x+iy)=a3-3ab2-ib3+i3a2bx+iy=a3-3ab2+i-b3+3a2b
comparing like terms
x=a3-3ab2,y=-b3+3a2b
Step 2: Put the value of xand y in the equation xa+yb:
xa+yb=a3-3ab2a+-b3+3a2bbxa+yb=a2-3b2-b2+3a2xa+yb=4a2-4b2xa+yb=4a2-b2
Hence, the correct option is (D)