University:
High School
Course:
High School Mathematics
Academic year:

2023
Views:

147

Pages:

2
Author:

anon

Mathematics: Complex Numbers- Modulus Argument Form We can combine the argument and modulus of a complex number in Modulus-Argument form, which is in the form: r= modulus θ = argument (usually expressed in radians) Alternatively, you can write it as: cis x is just an abbreviation for r(cos θ + isin θ) So is the modulus = 4, and the argument = π/2 Then we can write in Modulus-Argument form as: =4[cos(π/2) + isin(π/2)] Let’s solve a problem, and hopefully we can use the information and write it in Modulus-Argument form: For the complex number 4+4i, (a) Find the Modulus (b) Find the Argument (c) Write this complex number in Modulus-Argument Form (a) Modulus: a+bi = 4+2i a= 4, b=4 Modulus = √a2+b2 Modulus = √16+16 = √32 = 4√2 (b) Argument : tan θ =( b/a) tan θ = (4/4) =1 θ= (π/4) (c) Modulus-Argument form = r(cosθ + isinθ) Modulus = 4√2 Argument = (π/4) Therefore, the complex number 4+4i expressed in Modulus Argument form is : 4√2 [cos(π/4)+isin(π/4)] or 4√2 cis (π/4)