Maths AI HL · Euler form and integer powers

MATHS AI · HL · EULER FORM & POWERS

Teacher notes

Lesson sequence

Begin with the six oral questions, asking each student to explain one answer. Connect the powers prediction to the cis multiplication rule from the previous lesson.

Introduce Euler's formula, then let students work through conversions independently. Use the equivalent-arguments example to discuss the principal interval.

Develop de Moivre's theorem from repeated multiplication. Use the Argand diagram to connect the algebra to distance and direction.

Points to check

Students should raise the modulus to the power and multiply the argument by the power. A final argument may need adjusting by a multiple of 2π.

Check zero and negative powers before independent practice. Discuss selected solutions as a whole class.

The calculator pages are references. All examples use radians, and exact working should support the final answers.

Calculator instructions were checked against TI documentation; they have not been tested on a handheld or emulator.