Question

Simplify i⁶⁸
a) −i
b) 1
c) −1
d) i

Answer 1

To simplify i⁶⁸, divide the exponent by 4. Since 68 divided by 4 has zero remainder, i⁶⁸ simplifies to 1.

Step-by-step explanation:

To simplify i⁶⁸, we should first know that the powers of the imaginary unit i follow a pattern: i, i² = -1, i³ = -i, and i⁴ = 1. This pattern repeats every four powers, thus powers of i can be simplified by dividing the exponent by 4 and looking at the remainder to determine the equivalent value of i to a power of 1, 2, 3, or 4.

For the exponent 68, divide 68 by 4. The division equals 17 with a remainder of 0, suggesting i⁶⁸ is equivalent to i⁴ raised to the 17th power, which is 117, or simply 1.

Therefore, the simplification of i⁶⁸ is b) 1.

Answer 2

Option B

Step-by-step explanation:

Given that i⁶⁸ , assuming "i" refers to Iota.

On evaluation:

We know i = iota = -1

Clearly -1 get multiplied by each other 68 times.

We know 68 is a even number. In such cases, we get a positive number since it is divisible by 2 easily.

So i⁶⁸ = (-1)⁶⁸ = 1