How do I write a complex number in modulus-argument (polar) form?

• How do I multiply complex numbers in modulus-argument (polar) form?

• The main benefit of writing complex numbers in modulus-argument (polar) form is that they multiply and divide very easily
• How do I divide complex numbers in modulus-argument (polar) form?

• To?divide?two complex numbers in modulus-argument (polar) form, we?divide their moduli?and?subtract their arguments

How do we write a complex number in Euler's (exponential) form?

How do we multiply and divide complex numbers in Euler's form?

What are some common numbers in exponential form?

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

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

• To convert from modulus-argument (polar) form to Cartesian form
  • Write?z?=?r?(cosθ+ isinθ)as?z?=?r?cosθ+ (r?sinθ?)i
  • Find the values of the trigonometric ratios?r?sinθand?r?cosθ
    • You may need to use your knowledge of trig exact values
  • Rewrite as?z = a + bi where
    • a = r?cosθ and?b?=?r?sinθ
• To convert from exponential (Euler’s) form to Cartesian form first rewrite?z?=?r?e^iθin the form?z?=?r?cosθ+ (r?sinθ)i and then follow the steps above