Which subtraction expression has the difference 1 + 4i? This question may seem abstract at first, but it delves into the fascinating world of complex numbers and their arithmetic operations. In this article, we will explore various subtraction expressions and determine which one yields the difference 1 + 4i, thereby unraveling the mystery behind this intriguing mathematical concept.
Complex numbers are a fundamental part of mathematics, and they consist of a real part and an imaginary part. The imaginary part is represented by the letter ‘i’, which is defined as the square root of -1. Complex numbers are written in the form a + bi, where ‘a’ is the real part and ‘b’ is the imaginary part.
When performing subtraction with complex numbers, we subtract the real parts and the imaginary parts separately. In the given question, we are looking for a subtraction expression that results in the difference 1 + 4i. To achieve this, we need to find two complex numbers, let’s call them ‘z’ and ‘w’, such that z – w = 1 + 4i.
Let’s consider the following examples:
1. (5 + 3i) – (2 + i) = 3 + 2i
2. (7 + 2i) – (4 + 5i) = 3 – 3i
3. (8 + 6i) – (3 + 2i) = 5 + 4i
None of these examples yield the desired difference of 1 + 4i. Therefore, we must continue our search for the correct subtraction expression.
After further exploration, we discover the following expression:
4. (5 + 3i) – (4 + 1i) = 1 + 4i
In this case, the subtraction expression (5 + 3i) – (4 + 1i) results in the difference 1 + 4i, which is the answer we were seeking. This demonstrates that complex numbers can be subtracted in a straightforward manner, just like their real number counterparts.
In conclusion, the subtraction expression that has the difference 1 + 4i is (5 + 3i) – (4 + 1i). This example highlights the beauty and simplicity of complex number arithmetic, and it serves as a reminder of the importance of exploring various mathematical concepts to uncover their underlying principles.
