- Vanessa invested $2,500 into an account that will increase in value by 3.5% each year. What is the rate in this problem?” Your answer
- What is the additive identity of the complex number 14+5i?
The Correct Answer and Explanation is :
- The rate in the problem is 3.5%. This is the percentage by which Vanessa’s investment increases each year. The rate refers to the growth or increase in value relative to the initial amount, expressed as a percentage.
- The additive identity of a complex number is the number that, when added to any complex number, does not change the value of that complex number. In the case of the complex number 14 + 5i, the additive identity is 0 + 0i, or simply 0.
Here’s why:
In mathematics, the additive identity is the element that leaves other elements unchanged when added to them. For real numbers, the additive identity is 0, because adding 0 to any real number doesn’t change its value (e.g., 5 + 0 = 5). Similarly, in the set of complex numbers, the additive identity is the complex number 0 + 0i, which is simply the complex number 0.
A complex number is of the form a + bi, where a is the real part and bi is the imaginary part. The number 14 + 5i has a real part of 14 and an imaginary part of 5i. To add two complex numbers, you add the real parts together and the imaginary parts together. So, for example:
[
(14 + 5i) + (0 + 0i) = 14 + 5i
]
This shows that adding the additive identity (0 + 0i) to the complex number (14 + 5i) leaves it unchanged.
In conclusion, the additive identity of the complex number 14 + 5i is 0 or 0 + 0i. This is because adding 0 + 0i to any complex number will not alter its value, just as adding 0 to any real number does not change its value.