## Reflection: Complex Tasks De Moivre's Theorem - Section 3: Summarize

In the homework assignment for this section, a question came up where a complex number had a negative radius measure. The equation was z^3 = -125cis240° and students had to solve for z. Most students left the radius as -125 and got a new radius of -5 once they took the cube root. Their answers are shown on the left in this image. The answers from the textbook are shown on the right.

We had a great discussion about what a negative r value would mean in this context and if the answers that they got were equivalent to the answers that the book gave. After pressing them, students came up with a negative r value meaning that we need to go in the opposite direction of the direction angle, thus making the r value positive and adding 180° would be an equivalent complex number.

Once we arrived at this new knowledge, students could see that each root from the book answers (with a positive r) corresponded to a root from their answer (with a negative r).

# De Moivre's Theorem

Lesson 9 of 12

## Big Idea: How did mathematicians raise numbers to high powers before there were calculators?

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Subject(s):
Math, Precalculus and Calculus, Trigonometry, Law of Cosines, de Moivres Theorem, complex numbers
40 minutes

### Tim Marley

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