Check whether the statement is true or not :
`3 -: 4` i is a complex number.

Answer

To determine whether the statement "3 divided by 4i is a complex number" is true or not, we can follow these steps:

### Step 1: Understand the definition of complex numbers
A complex number is generally expressed in the form \( a + bi \), where \( a \) and \( b \) are real numbers, and \( i \) is the imaginary unit defined as \( i = \sqrt{-1} \).

### Step 2: Analyze the expression \( \frac{3}{4i} \)
We need to simplify the expression \( \frac{3}{4i} \). To do this, we can multiply the numerator and the denominator by \( i \) to eliminate the imaginary unit from the denominator.

### Step 3: Multiply by \( i \)
\[ \frac{3}{4i} \cdot \frac{i}{i} = \frac{3i}{4i^2} \]
Since \( i^2 = -1 \), we can substitute this into the expression:
\[ \frac{3i}{4(-1)} = \frac{3i}{-4} = -\frac{3}{4}i \]

### Step 4: Identify the form of the result
The result \( -\frac{3}{4}i \) can be expressed as \( 0 - \frac{3}{4}i \), which is in the form \( a + bi \) where \( a = 0 \) and \( b = -\frac{3}{4} \).

### Step 5: Conclusion
Since \( -\frac{3}{4}i \) is in the form of a complex number, we conclude that the statement "3 divided by 4i is a complex number" is true.

### Final Answer
The statement is true.

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