Understanding Complex Number Math: |iz^2|

Click For Summary
SUMMARY

The discussion focuses on calculating the absolute value of the expression |iz^2| where z is represented in polar form as z=rcis(theta). The key identity used is |z_1z_2|=|z_1|·|z_2|, which simplifies the calculation by allowing the separation of components. The absolute value of the imaginary unit i is established as 1, which is crucial for solving the problem. This understanding is essential for correctly incorporating i into the absolute value calculation.

PREREQUISITES
  • Understanding of complex numbers and their polar representation
  • Familiarity with the properties of absolute values in complex arithmetic
  • Knowledge of basic trigonometric functions
  • Ability to manipulate algebraic expressions involving complex variables
NEXT STEPS
  • Study the properties of complex numbers, focusing on polar and rectangular forms
  • Learn about the geometric interpretation of complex multiplication
  • Explore the concept of absolute value in complex analysis
  • Review the application of complex identities in solving equations
USEFUL FOR

Students of mathematics, particularly those studying complex analysis, educators teaching complex number concepts, and anyone seeking to deepen their understanding of complex arithmetic operations.

sweeper
Messages
1
Reaction score
0
Complex numbers
If z=rcis(theta) FIND: |iz^2|
I am confused about how I incorporate the i into the absolute value. I can't remember what it means. Please help and show exactly how I complete the workings. I can easily find the absolute value of z^2 I just really don't understand how to put the i into it.
Thank you!
 
Physics news on Phys.org
Hi, and welcome to the forum.

You should use the identity $|z_1z_2|=|z_1|\cdot|z_2|$. For the rest, please see this section on Wikipedia.
 
The absolute value of i is 1!
 

Similar threads

MHB Polar Representation of a Complex Number
  • · Replies 5 ·
Replies
5
Views
2K
High School Is this a complex number at the second quadrant?
  • · Replies 7 ·
Replies
7
Views
2K
MHB Max Value of |bc| for Complex Numbers in Inequality
  • · Replies 2 ·
Replies
2
Views
2K
Undergrad Is it valid to express a complex number as a vector?
  • · Replies 8 ·
Replies
8
Views
2K
High School Principal square root of a complex number, why is it unique?
  • · Replies 13 ·
Replies
13
Views
6K
MHB Finding Real Part of $z$ for Complex Numbers
  • · Replies 1 ·
Replies
1
Views
1K
MHB Complex Numbers - from Polar to Algebraic
  • · Replies 2 ·
Replies
2
Views
2K
High School How can complex numbers be elevated to complex powers?
  • · Replies 12 ·
Replies
12
Views
3K
High School Getting from complex domain to real domain
  • · Replies 3 ·
Replies
3
Views
2K
MHB Ap1.3.51 are complex numbers, show that
  • · Replies 4 ·
Replies
4
Views
2K