Why is \( (1 + \sqrt{-5}) \times (1 - \sqrt{-5}) \) Equal to 6?

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In summary, the question being discussed is why the expression (1 + sqrt(-5)) x (1 – sqrt(-5)) is equal to 6. The conversation also touches on the use of imaginary numbers in solving the problem, as well as a typo in the original question. Ultimately, the solution is found by expanding the expression and simplifying it using the formula for the difference of squares. The conversation is now closed due to lack of effort from the original poster.
  • #1
harrylentil
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Why is (1 + sqrt(-5) x (1 – sqrt(-5)) equal to 6?
 
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  • #2
Did you expand the expression?

Do you know about imaginary numbers? You don't have to to calculate the expression, but it helps understanding what is going on.
 
  • #3
I don't know how to work with imaginary numbers.
 
  • #4
Then just imagine that sqrt(-5) is some number that you don't know. You don't have to use imaginary numbers to solve the problem.
 
  • #5
Typo in my original question - a right bracket is missing. It should be,
Why is (1 + sqrt(-5)) x (1 – sqrt(-5)) equal to 6?

Anyone?
 
  • #6
mfb said:
Did you expand the expression?
 
  • #7
You just have a difference of squares: (a+b)(a-b) = a^2-b^2 which, in your case means: (1 + sqrt(-5)) (1 – sqrt(-5)) = 1 - (-5)
 
  • #8
Since Juan has shown the OP how to do this, and the OP keeps refusing to show any effort, this thread is now closed (after some cleanup)
 

FAQ: Why is \( (1 + \sqrt{-5}) \times (1 - \sqrt{-5}) \) Equal to 6?

How do you calculate simple addition?

To calculate simple addition, you need to add two or more numbers together. For example, to calculate 2 + 3, you would add 2 and 3 to get a total of 5. This is the basic concept of addition.

What is the order of operations in a simple calculation?

The order of operations in a simple calculation is often remembered through the acronym PEMDAS, which stands for Parentheses, Exponents, Multiplication, Division, Addition, and Subtraction. This means that when solving a calculation, you should first solve any operations within parentheses, then any exponents, followed by multiplication and division from left to right, and finally addition and subtraction from left to right.

How do I know which number to put first in a subtraction calculation?

In a subtraction calculation, the first number written is the number you are subtracting from, or the minuend. The second number written is the number you are subtracting, or the subtrahend. For example, in 5 - 3, 5 is the minuend and 3 is the subtrahend. This means that you are subtracting 3 from 5 to get a difference of 2.

What is the difference between a simple calculation and a complex calculation?

A simple calculation involves basic mathematical operations such as addition, subtraction, multiplication, and division, and can be solved using mental math or a calculator. A complex calculation involves more advanced operations, such as logarithms, trigonometric functions, or algebraic equations, and may require multiple steps to solve.

Can you explain the concept of carrying in a simple calculation?

Carrying is a concept in addition where if the sum of two numbers is greater than 9, you add the extra digit to the next column. For example, in 23 + 9, the sum of 3 and 9 is 12, which is greater than 9. So, you carry the 1 to the next column and write the 2 below the line. This results in an answer of 32.

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