Power of i Calculator

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Table of Contents

1

What is Power of i?

Powers of the imaginary unit repeat in a cycle of four.

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How to Use This Calculator

  1. Enter or select Exponent n.
  2. Check the unit beside each measurement. For a percentage or rate, use the scale and time period stated in the form.
  3. Choose Calculate, then compare the output with the formula and example below. If you change a value or option, calculate again to update the result.
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Formula Used

i^0 = 1; i^1 = i; i^2 = −1; i^3 = −i; i^4 = 1
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Variables Explained

InputWhat it means
Exponent nUse the measured or stated value for this item, with the unit or category shown beside the field.
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Worked Example

11 mod 4 = 3, so i^11 = −i.

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Why Use This Calculator?

Reduce a complex-number expression by recognizing its four-term repeating pattern.

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Common Mistakes

    • Reduce the exponent modulo four before choosing the matching value.
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Frequently Asked Questions

Should I round numbers before calculating?

Keep the original input precision through the calculation and round the final answer to the precision you need. Rounding an intermediate result can change later steps.

Why can a manual calculation differ slightly?

Check the operation, units, signs and rounding first. Equivalent fractions or expressions can look different while representing the same value.

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Sources & References

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