MHB Understanding Complex Number Math: |iz^2|

AI Thread Summary
To find |iz^2| for a complex number z=rcis(theta), use the identity |z_1z_2|=|z_1|·|z_2|. The absolute value of i is 1, which simplifies the calculation. First, determine |z^2|, then multiply it by |i| to find |iz^2|. Understanding these properties of absolute values in complex numbers is crucial. This approach clarifies how to incorporate i into the absolute value calculation.
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!
 
Mathematics 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!
 
Seemingly by some mathematical coincidence, a hexagon of sides 2,2,7,7, 11, and 11 can be inscribed in a circle of radius 7. The other day I saw a math problem on line, which they said came from a Polish Olympiad, where you compute the length x of the 3rd side which is the same as the radius, so that the sides of length 2,x, and 11 are inscribed on the arc of a semi-circle. The law of cosines applied twice gives the answer for x of exactly 7, but the arithmetic is so complex that the...
Just chatting with my son about Maths and he casually mentioned that 0 would be the midpoint of the number line from -inf to +inf. I wondered whether it wouldn’t be more accurate to say there is no single midpoint. Couldn’t you make an argument that any real number is exactly halfway between -inf and +inf?

Similar threads

Replies
5
Views
2K
Replies
7
Views
3K
Replies
7
Views
2K
Replies
2
Views
1K
Replies
13
Views
2K
Replies
1
Views
1K
Replies
2
Views
2K
Back
Top