Imaginary multiplication with answer to be in polar (variables)

Click For Summary
SUMMARY

The discussion focuses on multiplying two complex numbers in polar form, specifically (a+bi)(c+di) where b, c, d > 0 and a < 0. The user initially converts the complex numbers to polar form using the formula (r cis θ), where r is the modulus and θ is the argument. The multiplication of these polar forms leads to a complex number that requires finding its modulus and argument using the Pythagorean theorem and the arctangent function.

PREREQUISITES
  • Understanding of complex numbers and their representation in polar form.
  • Familiarity with the Pythagorean theorem for calculating modulus.
  • Knowledge of the arctangent function for determining arguments.
  • Basic algebraic manipulation of complex numbers.
NEXT STEPS
  • Learn how to convert complex numbers from rectangular to polar form.
  • Study the multiplication of complex numbers in polar form.
  • Research methods for calculating the modulus and argument of a complex number.
  • Explore the properties of complex numbers, including their geometric interpretations.
USEFUL FOR

Students and professionals in mathematics, physics, and engineering who are working with complex numbers, particularly in fields involving signal processing or electrical engineering.

sportsguy3675
Messages
45
Reaction score
0
I have to find (a+bi)(c+di) in polar form given that b,c,d>0 and a<0.

So I convert each one to polar first.

[tex]( (a+b)cis(\arctan(-b/a) + \pi) ) ( (c+d)cis(\arctan(d/c)) )[/tex]

That's as far as I got. Little help please?
 
Last edited:
Physics news on Phys.org
Multiply the numbers out first. Then you will have just one complex number. Then just find the modulus and argument using pythagoras and arctan like you mentioned.
 
That would give -(ac) -(adi) +(bci) -(bd)?

But how do I find a modulus and argument with that?
 

Similar threads

  • · Replies 11 ·
Replies
11
Views
3K
  • · Replies 3 ·
Replies
3
Views
3K
  • · Replies 12 ·
Replies
12
Views
3K
  • · Replies 7 ·
Replies
7
Views
1K
  • · Replies 24 ·
Replies
24
Views
2K
  • · Replies 0 ·
Replies
0
Views
1K
Replies
4
Views
2K
Replies
17
Views
3K
Replies
39
Views
6K
Replies
8
Views
2K