Question

What is the value of the expression i To the power of 1 times I to the power of 2 times I to the power of 3 times I to the power of 4

Answer 1

The value of the expression i to the power of 1 times i to the power of 2 times i to the power of 3 times i to the power of 4 is 1. This is found by recognizing that i squared is -1, i cubed is -i, and i to the fourth power is 1; then applying the multiplication of these four terms sequentially.

Step-by-step explanation:

The student's question pertains to evaluating the expression i to the power of 1, i to the power of 2, i to the power of 3, and i to the power of 4, all multiplied together. The value of the imaginary unit i is defined as the square root of -1.

When calculating with powers of the imaginary unit i, we can use the powers' distinct values:

• i to the power of 1 is i,
• i to the power of 2 is -1,
• i to the power of 3 is -i, and
• i to the power of 4 is 1.

Thus, the expression can be simplified by multiplying these values in succession:

(i) × (-1) × (-i) × (1) = i × (-i) = -1 × (i²) = -1 × (-1) = 1.

The value of the given expression is 1.

Answer 2

-1

Step-by-step explanation:

`i^1\cdot i^2\cdot i^3\cdot i^4= \\\\i^(1+2+3+4)= \\\\i^(10)= \\\\-1`

Hope this helps!