Simplify the following
`(21)/(14i)`

Answer

To simplify the expression \(\frac{21}{14i}\), we can follow these steps:

### Step 1: Multiply by \(\frac{i}{i}\)
To eliminate the imaginary unit \(i\) from the denominator, we multiply both the numerator and the denominator by \(i\):

\[ \frac{21}{14i} \cdot \frac{i}{i} = \frac{21i}{14i^2} \]

### Step 2: Simplify the denominator
Recall that \(i^2 = -1\). Therefore, we can substitute \(-1\) for \(i^2\):

\[ \frac{21i}{14(-1)} = \frac{21i}{-14} = -\frac{21i}{14} \]

### Step 3: Simplify the fraction
Now, we can simplify the fraction \(-\frac{21i}{14}\) by dividing both the numerator and the denominator by their greatest common divisor, which is 7:

\[ -\frac{21i}{14} = -\frac{21 \div 7}{14 \div 7} = -\frac{3i}{2} \]

### Final Answer
Thus, the simplified form of \(\frac{21}{14i}\) is:

\[ -\frac{3i}{2} \]

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