Answer :
Certainly! Let's break down the simplification process for each expression step-by-step:
### 1. Simplify [tex]\(5i - 7 + 8i + 10 + i\)[/tex]
Step 1: Combine the imaginary parts.
- You have [tex]\(5i\)[/tex], [tex]\(8i\)[/tex], and [tex]\(i\)[/tex]. To combine these, add them together:
[tex]\[
5i + 8i + i = 14i
\][/tex]
Step 2: Combine the real numbers.
- The real numbers in the expression are [tex]\(-7\)[/tex] and [tex]\(10\)[/tex]. Add them:
[tex]\[
-7 + 10 = 3
\][/tex]
Final Expression:
- Combine the real part and the imaginary part:
[tex]\[
3 + 14i
\][/tex]
### 2. Simplify [tex]\((5)(i+3) + 3i - 8\)[/tex]
Step 1: Distribute within the parentheses.
- Distribute the [tex]\(5\)[/tex] into [tex]\((i+3)\)[/tex]:
[tex]\[
5(i + 3) = 5i + 15
\][/tex]
Step 2: Combine all like terms.
- Combine [tex]\(5i\)[/tex] with [tex]\(3i\)[/tex]:
[tex]\[
5i + 3i = 8i
\][/tex]
- Combine the real numbers [tex]\(15\)[/tex] and [tex]\(-8\)[/tex]:
[tex]\[
15 - 8 = 7
\][/tex]
Final Expression:
- Combine the real part and the imaginary part:
[tex]\[
7 + 8i
\][/tex]
Summary:
- The simplified form of the first expression is [tex]\(3 + 14i\)[/tex].
- The simplified form of the second expression is [tex]\(7 + 8i\)[/tex].
Feel free to ask if you have more questions or need further clarification!
### 1. Simplify [tex]\(5i - 7 + 8i + 10 + i\)[/tex]
Step 1: Combine the imaginary parts.
- You have [tex]\(5i\)[/tex], [tex]\(8i\)[/tex], and [tex]\(i\)[/tex]. To combine these, add them together:
[tex]\[
5i + 8i + i = 14i
\][/tex]
Step 2: Combine the real numbers.
- The real numbers in the expression are [tex]\(-7\)[/tex] and [tex]\(10\)[/tex]. Add them:
[tex]\[
-7 + 10 = 3
\][/tex]
Final Expression:
- Combine the real part and the imaginary part:
[tex]\[
3 + 14i
\][/tex]
### 2. Simplify [tex]\((5)(i+3) + 3i - 8\)[/tex]
Step 1: Distribute within the parentheses.
- Distribute the [tex]\(5\)[/tex] into [tex]\((i+3)\)[/tex]:
[tex]\[
5(i + 3) = 5i + 15
\][/tex]
Step 2: Combine all like terms.
- Combine [tex]\(5i\)[/tex] with [tex]\(3i\)[/tex]:
[tex]\[
5i + 3i = 8i
\][/tex]
- Combine the real numbers [tex]\(15\)[/tex] and [tex]\(-8\)[/tex]:
[tex]\[
15 - 8 = 7
\][/tex]
Final Expression:
- Combine the real part and the imaginary part:
[tex]\[
7 + 8i
\][/tex]
Summary:
- The simplified form of the first expression is [tex]\(3 + 14i\)[/tex].
- The simplified form of the second expression is [tex]\(7 + 8i\)[/tex].
Feel free to ask if you have more questions or need further clarification!
