Question

Find the value of i^39
A)-i
B)i
C)1
D)-1

Answer 1

Answer:

A) -i

Step-by-step explanation:

The powers of i have a repetitive cyclic nature. When we raise the imagenry unit i to increasing powers, we get a pattern which repeats itself and is four members long.

When asked to determine the value of i to a power higher than 4, we can use this information in order to find our position in the cycle.

So, instead of using the actual power, we can take the remainder of the power divided by 4.

39/4 = 9 remainder 3

Using above knowledge

¡³⁹ = (i⁴)⁹ × i³

= (i)⁹ × i³

= 1 × i³

= i³

= -i