If (^{1 + i}/_{1 - i})^m = 1, then find the least positive integral value of m.

 

(^{1 + i}/_{1 - i})^m = 1

⇒ (^{(1 + i)(1 + i)}/_{(1 - i)(1 + i)})^m

= (^{1 + 2i + i2}/_{1 - i²})^m

= (^{1 + 2i - 1}/_{1 + 1})^m

= (²ⁱ/₂)^m = (i)^m

So, i^m = 1

Now, i¹ = i, i² = -1, i³ = -i, i⁴ = 1

∴ m must be a multiple of 4

Therefore, the least positive integral value of m = 4