Multiply moduli, add arguments: To multiply two complex numbers in polar form: multiply the moduli and add the arguments.
Geometrically, multiplying by r cisθ scales by r and rotates by θ.
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IB-style question — multiply in polar form
Find (2 cis(π/6))(3 cis(π/4)), giving your answer in polar form.
Step by step
- Multiply the moduli.
- Add the arguments.
- Combine.
Final answer
6 cis(5π/12).
Divide moduli, subtract arguments: To divide, divide the moduli and subtract the arguments (top minus bottom). Much easier than the conjugate method when you're already in polar form.
IB-style question — divide in polar form
Find (12 cis(2π/3))/(4 cis(π/4)), giving your answer in polar form.
Step by step
- Divide the moduli.
- Subtract the arguments (top − bottom).
- Combine.
Final answer
3 cis(5π/12).