Answer:
Explanation:
I am came across a problem that asked me to find the magnitude of a complex number:
|4+3i|
After reading online and the textbook, I figured out the question could be solved by finding the distance of the complex number from the origin on a complex plane. As so:
enter image description here
I understand this so far. However, my trouble is that when I solve, using the Pythagorean theorem:
42+(3i)2−−−−−−−−√=16+9i2−−−−−−−√=16−9−−−−−√=7–√
I end up getting the incorrect solution (the correct solution is 5). Now, when I plug |4+3i|
into my TI-84, I get 5 as a result. I did some research into the magnitudes of absolute values and saw that they can be found by taking the square root of the product of the complex conjugate pair. Solving it this way, I also got 5 as a solution. I am confused as to why the absolute value of a complex number is treated so differently to that of a real number. Why is this and what is the correct way to solve for the magnitude of a complex number?
Edit:
Thanks for all the responses. I'm still having trouble understanding how you can ignore the i
when looking at the distance from 0
to 3i
. I attempted to draw a diagram to better understand this: