Solving Complex Expressions: 1/z^2 & 1/z^3

In summary, the conversation discusses finding the values of 1/z^2 and 1/z^3, where z=1+2i. One approach is to multiply by the conjugate, but it is also suggested to calculate 1/z first before calculating powers. The conversation also includes a brief discussion on the difference between 1/z^2 and (1/z)^2.
  • #1
ENGR_student
6
0
Hello I'm studying complex numbers for class and the question is stated as:
Let z=1+2i
Find:
a) 1/z^2
b) 1/z^3

I was thinking just to multiply by the conjugate (1-2i)^2 for (a) and similarly for (b).
Would that be correct in solving it?
 
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  • #2
You can do that, right.
Alternatively, calculate 1/z first, and then calculate powers of that.

As this looks like homework, I moved your thread.
 
  • #3
Oh thank you!
I apologize if I put it in the wrong thread!
 
  • #4
ENGR_student said:
Oh thank you!
I apologize if I put it in the wrong thread!
Firstly, let's establish what you are actually asking.

For example, the way you wrote it, 1/z^2 = [itex]\frac{1}{z^2}[/itex], NOT [itex](\frac{1}{z})^2[/itex]

EDIT: Please ignore. Complete brain-fart by me there! :redface:
 
Last edited:
  • #5
oay said:
For example, the way you wrote it, 1/z^2 = [itex]\frac{1}{z^2}[/itex], NOT [itex](\frac{1}{z})^2[/itex]
Where is the difference?
 
  • #6
mfb said:
Where is the difference?
Thanks. I simply cannot believe what I wrote in my previous post.

I blame lack of sleep...:zzz:
 
  • #7
Surely there must be some way to completely delete a post so that those of us who post a really stupid idea can pretend it never happened!?
 

What is the definition of a complex expression?

A complex expression is a mathematical expression that includes both real and imaginary numbers. It can involve multiple operations such as addition, subtraction, multiplication, and division.

How do you simplify complex expressions?

To simplify complex expressions, you must first perform any operations inside parentheses, then work from left to right to simplify any remaining operations. You can also use rules of exponents and properties of logarithms to simplify further.

What is the difference between 1/z^2 and 1/z^3?

Both 1/z^2 and 1/z^3 are complex expressions involving the variable z. The main difference is the exponent - while 1/z^2 involves squaring the variable, 1/z^3 involves cubing the variable. This results in different solutions when the expressions are simplified.

How are complex expressions used in science?

Complex expressions are used in science to describe and model real-world phenomena. They are particularly useful in physics, chemistry, and engineering, where they can be used to analyze and predict the behavior of complex systems.

What are some tips for solving complex expressions involving fractions?

When solving complex expressions involving fractions, it can be helpful to find a common denominator, simplify any fractions within the expression, and use the distributive property. It is also important to be familiar with the rules of exponents and properties of logarithms.

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