Multiply & divide in polar form
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Flip to reveal answersHow do you multiply complex numbers in polar form?
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All 8 Flashcards — Multiply & divide in polar form
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Question
How do you multiply complex numbers in polar form?
Answer
Multiply the moduli and add the arguments: r₁r₂ cis(θ₁ + θ₂).
Question
How do you divide complex numbers in polar form?
Answer
Divide the moduli and subtract the arguments: (r₁/r₂) cis(θ₁ − θ₂).
Question
What does multiplying by r cisθ do geometrically?
Answer
Scales the point by r and rotates it by θ about the origin.
Question
What does multiplying by i do on the Argand diagram?
Answer
Rotates 90° anticlockwise (i = cis(π/2), modulus 1).
Question
(2 cis(π/6))(3 cis(π/4)) = ?
Answer
6 cis(5π/12) — moduli 2×3 = 6, arguments π/6 + π/4 = 5π/12.
Question
(12 cis(2π/3))/(4 cis(π/4)) = ?
Answer
3 cis(5π/12) — moduli 12÷4 = 3, arguments 2π/3 − π/4 = 5π/12.
Question
Common mistake multiplying in polar form?
Answer
Adding the moduli or multiplying the arguments. It's moduli × and arguments +.
Question
Why is polar form good for products?
Answer
Multiplying just scales and rotates, so it needs only one multiply and one add — no FOIL.
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Full study notes for Multiply & divide in polar form
Topic 1.13 hub
Complex numbers: polar (HL only)
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