# Finding the absolute value (modulus) and solving equation

• infiniteking1
In summary, the problem involves finding the absolute value of a complex number using the formula |a+bi|=sqrt(a^2+b^2). The value of i is 1 and it is included when finding the square root. The final answer is correct and there is no need to simplify the expression any further.
infiniteking1
1. | (2-i)(3+2i)(-5-6i)(-7+3i) / (-4+i) |

## Homework Equations

3. I am pretty sure I am not computing it right but this is what i come up with.

square root of 5* square root of 13* square root of 61* square root of 58 / square root of 17.

I'm really sure you are computing it right. |a*b|=|a|*|b|, yes? Why do you think it's not right?

I'm not sure if the value of i by itself is 1 or whether or not to include it when I am finding the square root.

infiniteking1 said:
I'm not sure if the value of i by itself is 1 or whether or not to include it when I am finding the square root.

The absolute value of a+bi where a and b are both real is sqrt(a^2+b^2). It's the length of the hypotenuse of the triangle with real side a and imaginary perpendicular side b in the Argand diagram. It's the pythagorean theorem. |1|=1 and |i|=1. You are doing everything correctly. Trust me.

Ok, thanks for the help. Making sure but there's nothing more to do to this problem, correct?

infiniteking1 said:
Ok, thanks for the help. Making sure but there's nothing more to do to this problem, correct?

Not really. You could collect the square roots, or you could write it as an approximate decimal. But I don't see any reason to do that.

## 1. What is the absolute value (modulus) of a number?

The absolute value of a number is the distance of that number from 0 on a number line. It is always a positive value, regardless of the sign of the original number.

## 2. How do I find the absolute value of a number?

To find the absolute value of a number, you can simply remove the negative sign if the number is negative. If the number is positive, the absolute value is the same as the original number.

## 3. How do I solve an equation involving absolute value?

To solve an equation involving absolute value, you need to consider two cases: when the expression inside the absolute value is positive and when it is negative. You can then solve for both cases and check the solutions to see which ones satisfy the original equation.

## 4. Can absolute value be applied to complex numbers?

Yes, absolute value can be applied to complex numbers. The absolute value of a complex number is the square root of the sum of the squares of its real and imaginary parts.

## 5. Is the absolute value function continuous?

Yes, the absolute value function is continuous. This means that as the input to the function changes, the output also changes continuously without any abrupt jumps or breaks.

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