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Where would you use additive inverse in real life?
When you owe money
When can you say that a given real number is irrational?
A real number is an irrational number if it cannot be expressed as a fraction a/b, where a and b are integers. Most real numbers are irrational. The most well known irrational numbers are π and √2. The inverse condition are called the rational numbers.
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.
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.
Why 0 does not have a multiplicative inverse?
As n gets very small, 1/n goes towards infinity. A multiplicative inverse of 0 would be some number x, such that 0x=1. This is impossible with the real numbers we use, since 0x=0 for any number x. One might be tempted to invent a new number (calling it "infinity", "nullity", or any other name) that would be the inverse of 0. Of course, then you're not dealing with real numbers anymore, you're dealing with real numbers plus this invented number. There are serious issues even with this approach. Again, let x be this "multiplicative inverse of 0". Then 0*1=0 and 0*2=0. So 0*1 = 0*2. Multiply both sides by x to get x*0*1 = x*0*2. Since x*0 is 1, this means 1*1 = 1*2. So 1=2, which is an absurd conclusion. As you can see, there are good reasons not to allow a multiplicative inverse for 0 - it breaks all the laws of multiplication we're accustomed to.
