Mathematics 10 — Exercise Review · Q3 (ii)

Full question

Simplify the following expression.

Step-by-step solution

1. Add powers when multiplying the same base: 13 + 11 = 24.

2. By definition, the square of iota is −1.

   $$i^2=-1$$

3. Multiply i² by i to obtain i³.

   $$i^3=-i$$

4. Square i² to obtain i⁴: (−1) × (−1) = 1.

   $$i^4={\left(-1\right)}^2$$

5. Divide 24 by 4: 24 = 4 × 6 + 0.

   $$i^{24}=i^0\times {\left(i^4\right)}^6$$

6. Every i⁴ contributes 1. Substitute the value of the remaining power.

   $$i^{24}=1^6\times 1$$

7. The simplified value is therefore:

   $$i^{24}=1$$

Answer

The final answer is shown below.