Florida B.E.S.T. MA.912.NSO.2.6
The Standard
Rewrite complex numbers to trigonometric form. Multiply complex numbers in trigonometric form.
Florida B.E.S.T. Standards for Mathematics
Teacher's field guide
What This Standard Means
What Students Need to Do
- Students convert a complex number from rectangular form to trigonometric form using its modulus and argument. They multiply complex numbers by multiplying moduli and adding arguments.
What Mastery Looks Like
- Students correctly find the modulus and argument of a complex number and write its trigonometric form. They multiply moduli, add arguments, and give an equivalent angle in the requested interval.
Common Misconceptions
- Students may use arctangent without checking the quadrant, which gives the wrong angle. They may confuse the modulus with its square or multiply angles instead of adding them.
How to Assess It
- Give students z₁ = 2(cos 30° + i sin 30°) and z₂ = 3(cos 45° + i sin 45°). Ask them to find z₁z₂ in trigonometric form and explain each step.
Lesson moves
Ways to Teach It
Plot complex numbers on graph paper, measure each modulus and angle, then write the matching trigonometric form.
Ask students to explain why multiplying complex numbers changes both distance from the origin and angle.
Play a matching game with cards showing rectangular forms, trigonometric forms, products, and points on the complex plane.
Model two rotations and scale changes using a navigation vector, then connect the combined movement to complex multiplication.
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Printable MA.912.NSO.2.6 Worksheet
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Related Standards
- MA.912.T.1.7
Simplify expressions using trigonometric identities.
- MA.912.NSO.3.2
Represent vectors in component form, linear form or trigonometric form. Rewrite vectors from one form to another.
- MA.912.AR.1.8
Rewrite a polynomial expression as a product of polynomials over the real or complex number system.
- MA.912.T.2
Extend trigonometric functions to the unit circle.
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