Answer:
10i
Explanation:
8-7=1
7-6=1
The real part of the complex numbers is following an arithmetic progression with first term 8 and common difference 1.
………………………………………
-6+2=-4
-4+2=-2
THe Imaginary part of the complex numbers is following an arithmetic progression with first term -6 and common difference 2.
………………………………………
Then the term she of the sequence can be written:
(8 - n) + i(-6 + 2n)
………………………………………
We get a purely imaginary term when its real part is nul :
⇒ 8 - n = 0
⇒ 8 = n
………………………………………
If we take n = 8
⇒ -6 + 2n = -6 + 2×8 = -6 + 16 = 10
Therefore,
The term of the arithmetic progression 8 - 6i, 7 – 4i, 6 — 2i, ... which is purely imaginary is :
10i