Mathematics 10 — Exercise Review · Q3 (i)

Full question

Simplify the following expression.

Step-by-step solution

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

   $$i^2=-1$$

2. Multiply i² by i to obtain i³.

   $$i^3=-i$$

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

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

4. Divide 37 by 4: 37 = 4 × 9 + 1.

   $$i^{37}=i^1\times {\left(i^4\right)}^9$$

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

   $$i^{37}=1^9\times i$$

6. The simplified value is therefore:

   $$i^{37}=i$$

Answer

The final answer is shown below.