Simplify the following powers of i : a) \( i^{19}=\square \) b) \( i^{38}=\square \) c) \( i^{86}=\square \) d) \( i^{108}=\square \) e) \( i^{1319}=\square \)

Simplify the expression by following steps: - step0: Solution: \(i^{1319}\) - step1: Evaluate: \(i^{4\times 329+3}\) - step2: Evaluate: \(\left(i^{4}\right)^{329}i^{3}\) - step3: Calculate: \(1^{329}\times i^{3}\) - step4: Calculate: \(i^{3}\) - step5: Calculate: \(i^{2}\times i\) - step6: Calculate: \(-i\) Calculate or simplify the expression \( i^38 \). Simplify the expression by following steps: - step0: Solution: \(i^{38}\) - step1: Evaluate: \(i^{4\times 9+2}\) - step2: Evaluate: \(\left(i^{4}\right)^{9}i^{2}\) - step3: Calculate: \(1^{9}\times i^{2}\) - step4: Calculate: \(i^{2}\) - step5: Evaluate the power: \(-1\) Calculate or simplify the expression \( i^86 \). Simplify the expression by following steps: - step0: Solution: \(i^{86}\) - step1: Evaluate: \(i^{4\times 21+2}\) - step2: Evaluate: \(\left(i^{4}\right)^{21}i^{2}\) - step3: Calculate: \(1^{21}\times i^{2}\) - step4: Calculate: \(i^{2}\) - step5: Evaluate the power: \(-1\) Calculate or simplify the expression \( i^19 \). Simplify the expression by following steps: - step0: Solution: \(i^{19}\) - step1: Evaluate: \(i^{4\times 4+3}\) - step2: Evaluate: \(\left(i^{4}\right)^{4}i^{3}\) - step3: Calculate: \(1^{4}\times i^{3}\) - step4: Calculate: \(i^{3}\) - step5: Calculate: \(i^{2}\times i\) - step6: Calculate: \(-i\) Calculate or simplify the expression \( i^108 \). Simplify the expression by following steps: - step0: Solution: \(i^{108}\) - step1: Evaluate: \(i^{4\times 27}\) - step2: Calculate: \(1^{27}\) - step3: Calculate: \(1\) Let's simplify the powers of \( i \): a) \( i^{19} = -i \) b) \( i^{38} = -1 \) c) \( i^{86} = -1 \) d) \( i^{108} = 1 \) e) \( i^{1319} = -i \) In summary: - \( i^{19} = -i \) - \( i^{38} = -1 \) - \( i^{86} = -1 \) - \( i^{108} = 1 \) - \( i^{1319} = -i \)