Conversion between Forms of Complex Numbers (DP IB Applications & Interpretation (AI)): Revision Note

Conversion of Forms

Converting from Cartesian form to modulus-argument (polar) form or exponential (Euler's) form

• To convert from Cartesian form to modulus-argument (polar) form or exponential (Euler) form use 

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Converting from modulus-argument (polar) form or exponential (Euler's) form to Cartesian form

• To convert from modulus-argument (polar) form to Cartesian form

  • You may need to use your knowledge of trig exact values

  • a = r cosθ and b = r sinθ

  • Write z = r (cosθ + isinθ ) as z = r cosθ + (r sinθ )i

  • Find the values of the trigonometric ratios r sinθ and r cosθ

  • Rewrite as z = a + bi where

• To convert from exponential (Euler’s) form to Cartesian form first rewrite z = r e^iθ  in the form z = r cosθ + (r sinθ)i and then follow the steps above

Converting between complex number forms using your GDC

• Your GDC may also be able to convert complex numbers between the various forms

  • TI calculators, for example, have 'Convert to Polar' and 'Convert to Rectangular' (i.e. Cartesian) as options in the 'Complex Number Tools' menu

  • Make sure you are familiar with your GDC and what it can (and cannot) do with complex numbers