Question

2.4 complex numbers
score: 19/20 answered: 19/20
question 20
simplify \\(i^{24}\\)
1
-i
-1
i

Explanation:

Identify the properties of the imaginary unit

$$ i^1 = i,\quad i^2 = -1,\quad i^3 = -i,\quad i^4 = 1 $$

Divide the exponent by the cycle length

$$ 24 \div 4 = 6 \quad \text{with a remainder of } 0 $$

Evaluate the expression

$$ i^{24} = (i^4)^6 = 1^6 = 1 $$

Answer:

• 1 (Correct answer)
• -i
• -1
• i