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Answering the question in general terms:
1. Since we are taught the property at an early age (initially without identifying it formally as a property) , our use of it generally goes unnoticed (for example, when it occurs in a multiplication problem involving the digit 1).
2. When solving algebra or arithmetic problems or proofs, if we can reduce a factor to 1, then by the property we can eliminate this complicating factor.
3. Having identified this property, we can create new mathematical systems within which we can then decide whether or not to include that property.
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Is subtraction an identity property?
Subtraction is not an identity property but it does have an identity property. The identity is 0 and each number is its own inverse with respect to subtraction. However, this is effectively the same as the inverse property of addition so there is no real need to define it as a separate property.
What is the identity property for multiplications?
The identity property is the property that all numbers, real or imaginary, can be multiplied by 1 to obtain the same number; e.g., 14x1 = 14.
What is the multiplicative inverse of 4 plus i?
The multiplicative inverse of a complex number is the reciprocal of that number. To find the multiplicative inverse of 4 + i, we first need to find the conjugate of 4 + i, which is 4 - i. The product of a complex number and its conjugate is always a real number. Therefore, the multiplicative inverse of 4 + i is (4 - i) / ((4 + i)(4 - i)) = (4 - i) / (16 + 1) = (4 - i) / 17.
Why is the solution to an identity all real numbers?
That is how an identity is defined. If the solution was not true for all numbers, then it would not be called an identity. In fact, it should be true for all complex numbers as well.
What is a real life example of a cliff?
A real life example of a cliff are the white cliffs of Dover.
