The given equation is:

\[
2 + \frac{3}{4}j + \frac{1}{2}j = 2j
\]

Here, the equation involves complex numbers with the imaginary unit \( j \), where \( j^2 = -1 \).

Let's solve for \( j \).

### Step 1: Combine like terms

First, combine the terms involving \( j \):

\[
\frac{3}{4}j + \frac{1}{2}j = 2j
\]

To add these, convert the fractions to a common denominator:

\[
\frac{3}{4}j + \frac{1}{2}j = \frac{3}{4}j + \frac{2}{4}j = \frac{5}{4}j
\]

Now, substitute this back into the equation:

\[
2 + \frac{5}{4}j = 2j
\]

### Step 2: Isolate the imaginary terms

Move all terms involving \( j \) to one side of the equation:

\[
\frac{5}{4}j - 2j = -2
\]

Convert \( 2j \) into a fraction with the same denominator:

\[
\frac{5}{4}j - \frac{8}{4}j = -2
\]

Now, subtract the fractions:

\[
\frac{-3}{4}j = -2
\]

### Step 3: Solve for \( j \)

To isolate \( j \), multiply both sides by \( \frac{-4}{3} \):

\[
j = -2 \times \frac{-4}{3}
\]

Simplifying:

\[
j = \frac{8}{3}
\]

Thus, \( j = \frac{8}{3} \).

---

Do you want more details or have any questions?

Here are 5 related questions you might find helpful:
1. How do you solve equations with complex numbers?
2. What are the properties of imaginary numbers?
3. How can fractions be added or subtracted in equations?
4. What does it mean to combine like terms in algebraic expressions?
5. How do you simplify equations with fractions and variables?

**Tip:** Always aim to combine like terms to simplify an equation before solving!

Discover how to solve the equation 2 + 3/4j + 1/2j = 2j involving complex numbers and fractions. Learn how to combine like terms, handle fractions, and solve for the imaginary unit j. This problem is ideal for high school students, Grades 9-12.

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