Understanding Complex Number Math: |iz^2|

In summary, complex numbers are expressed in the form a + bi, plotted on a complex plane with real numbers on the horizontal axis and imaginary numbers on the vertical axis. The absolute value, or modulus, of a complex number is its distance from the origin on the complex plane and is calculated using the square root of the sum of the squares of the real and imaginary parts. To find the absolute value of iz^2, you can simplify it to a real number by expanding z^2 and factoring out the imaginary unit i. It can then be represented on a complex plane by plotting the initial complex number z and using the properties of absolute value or the Pythagorean theorem to determine the distance from the origin. The absolute value of iz
  • #1
sweeper
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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!
 
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  • #2
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.
 
  • #3
The absolute value of i is 1!
 

FAQ: Understanding Complex Number Math: |iz^2|

1. What are complex numbers and how are they represented?

Complex numbers are numbers that are expressed in the form a + bi, where a and b are real numbers and i is the imaginary unit, equal to the square root of -1. They are represented on a complex plane, with the real numbers plotted on the horizontal axis and the imaginary numbers plotted on the vertical axis.

2. What is the absolute value of a complex number?

The absolute value, or modulus, of a complex number is its distance from the origin on the complex plane. It is calculated by taking the square root of the sum of the squares of the real and imaginary parts: |a + bi| = √(a^2 + b^2).

3. How do you find the absolute value of iz^2?

To find the absolute value of iz^2, you first need to simplify it to a real number. This can be done by first expanding z^2 and then factoring out the imaginary unit i. The absolute value is then calculated as |iz^2| = |i||z^2| = |z^2|.

4. How do you represent |iz^2| on a complex plane?

To represent |iz^2| on a complex plane, you can plot the initial complex number z on the plane and then use the properties of absolute value to determine the distance from the origin. You can also use the Pythagorean theorem to calculate the distance directly from the real and imaginary parts of z.

5. What does the absolute value of iz^2 tell us about the complex number?

The absolute value of iz^2 tells us the distance of the complex number from the origin on the complex plane. It also gives us information about the magnitude and direction of the complex number, as well as its relation to the other complex numbers on the plane.

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