Math9-12+
Simplifying Powers of i Practice Set for Grade 9
By Linnea H.
A 10-problem practice worksheet that walks 9th graders through the four-value cycle of the imaginary unit i, with a worked example showing how to divide the exponent by 4 and use the remainder. It builds fluency with complex numbers and exponent patterns, and it is well suited to a short independent practice block or a warm-up.
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Teacher Guide & Tips
- Introduce the cycle of i (i, -1, -i, 1) on the board first, then have students work the worked example together before releasing them to the problems.
- Discussion question: Why does dividing the exponent by 4 give the same result as reducing the power to its remainder, and what happens when the remainder is 0?
- Scaffold for struggling readers: Provide a reference card listing the four powers of i and have them write the division step explicitly for each problem before simplifying.
- Extension for advanced students: Ask them to explain how the same cycle appears with negative exponents, such as simplifying i^(-3).
- Estimated time: About 20 to 25 minutes for the 10 problems, plus a few minutes for review.
Math9-12+
Simplifying Powers of i Practice Set for Grade 9
By Linnea H.
A 10-problem practice worksheet that walks 9th graders through the four-value cycle of the imaginary unit i, with a worked example showing how to divide the exponent by 4 and use the remainder. It builds fluency with complex numbers and exponent patterns, and it is well suited to a short independent practice block or a warm-up.
Customize for your classroom
Teacher Guide & Tips
- Introduce the cycle of i (i, -1, -i, 1) on the board first, then have students work the worked example together before releasing them to the problems.
- Discussion question: Why does dividing the exponent by 4 give the same result as reducing the power to its remainder, and what happens when the remainder is 0?
- Scaffold for struggling readers: Provide a reference card listing the four powers of i and have them write the division step explicitly for each problem before simplifying.
- Extension for advanced students: Ask them to explain how the same cycle appears with negative exponents, such as simplifying i^(-3).
- Estimated time: About 20 to 25 minutes for the 10 problems, plus a few minutes for review.