# Establish associative law of multiplication

• kathrynag
In summary, the associative law of multiplication is a mathematical property that states the grouping of numbers in a multiplication equation does not affect the result. The formula for this law is (a x b) x c = a x (b x c), and it allows us to change the grouping of numbers without changing the result. This property is important because it simplifies calculations and helps us understand the relationship between numbers and operations. It is applicable to all real numbers.
kathrynag

## Homework Statement

Establish associative law of multiplication by considering absolute values and arguements.
z1(z2z3)=(z1z2)z3

## The Attempt at a Solution

I think I need to use r(costheta +isintheta)
r1(costheta1+isintheta1)[r2r3(costheta2+isintheta2)(costheta3+isintheta3)]=
Is this just a bunch of multiplying out and showing it's the same?

Yes. The magnitudes multiply and the arguments add. Both operations are associative.

Ok, I think I see.

## What is the associative law of multiplication?

The associative law of multiplication is a mathematical property that states the way in which numbers are grouped together in a multiplication equation does not change the result.

## What is the formula for the associative law of multiplication?

The formula for the associative law of multiplication is (a x b) x c = a x (b x c), where a, b, and c are any real numbers.

## How does the associative law of multiplication work?

The associative law of multiplication works by allowing us to change the grouping of numbers in a multiplication problem without changing the result. This means that we can multiply any two numbers first, and then multiply the result by the third number, or we can multiply the first number by the product of the other two numbers.

## Why is the associative law of multiplication important?

The associative law of multiplication is important because it simplifies mathematical calculations by allowing us to regroup numbers in a multiplication equation without changing the result. It also helps us to better understand the relationship between numbers and operations.

## Is the associative law of multiplication applicable to all numbers?

Yes, the associative law of multiplication is applicable to all numbers, including whole numbers, fractions, decimals, and negative numbers. It is a fundamental property of multiplication that holds true for all real numbers.

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