⇒ You can write any complex number in terms of its modulus and argument

⇒ You can use the following rules to multiply complex numbers quickly when they are give in modulus-argument form

⇒ To prove thse results, consider Z₁ and Z₂ in modulus-argument form:

⇒ This complex number is in modulus-argument form, with modulus r₁r₂ and argument θ₁ + θ₂, as required

⇒ You can derive similar results for dividing two complex numbers given in modulus-argument form

⇒ Also see our notes on:

• Argand Diagrams
• Modulus and Argument
• Loci in the Argand Diagram
• Regions in the Argand Diagram