Question

(2i + 1) + (4i - 7)

Explanation:

Step1: Remove parentheses

To simplify \((2i + 1)+(4i - 7)\), we first remove the parentheses. Since there is a plus sign in front of the second parentheses, the signs of the terms inside remain the same. So we have \(2i + 1+4i - 7\).

Step2: Combine like terms

Next, we combine the like terms. The like terms for the imaginary part (with \(i\)) are \(2i\) and \(4i\), and the like terms for the real part are \(1\) and \(-7\). Combining the imaginary terms: \(2i+4i = 6i\). Combining the real terms: \(1 - 7=-6\)? Wait, no, wait, let's check again. Wait, the original expression is \((2i + 1)+(4i - 7)\). So \(2i+4i = 6i\) and \(1-7=-6\)? But that doesn't match the options. Wait, maybe there was a typo in the original problem? Wait, looking at the options, maybe the original problem is \((2i + 1)+(4i + 7)\)? Wait, no, the user's image shows \((2i + 1)+(4i - 7)\)? Wait, no, maybe I misread. Wait, the options include \(6i - 6\), \(2i - 8\), \(6i + 8\), etc. Wait, let's re - do the calculation.

Wait, if the expression is \((2i + 1)+(4i - 7)\):

Combine \(i\) terms: \(2i+4i = 6i\)

Combine constant terms: \(1+( - 7)=1 - 7=-6\)

So the result is \(6i-6\). But let's check the options. One of the options is \(6i - 6\). Wait, but let's check again.

Wait, maybe the original problem was \((2i + 1)+(4i + 7)\)? No, the user's image has \((4i - 7)\). Wait, let's check the steps again.

Step 1: Remove parentheses: \(2i + 1+4i - 7\)

Step 2: Combine like terms: \((2i + 4i)+(1 - 7)=6i-6\)

Answer:

\(6i - 6\) (assuming the option with \(6i - 6\) is one of the choices, for example, if the options are as shown, and the option with \(6i - 6\) is present, that's the answer)