Which term of the sequence 8-6i,7-4i,6-2i,...... is (i) purely real (ii) purely imaginary?

sequence of imaginary part, 6i, 4i, 2i, ...

to make the term real we must have, Im(part) = 0i = 0

since, 6i, 4i, 2i, ... forms an APwith a = 6i and c.d = -2i

so taking, t_n = 0 = a+(n-1)d

0 = 6i + (n - 1 ) (-2i)

n = -6i/-2i + 1 = 3 +1 = 4

hence the real term is the 4rth term..ans

semilerly, imaginary term = t_n=a + (n-1)d

0=8+(n-1)(-1)

8-n+1=0

n=9

hence, imginary term =9th term.