Simplify (34i)/(17i)

Solution:

Step 1: Identify and eliminate common numerical factors.

• Step 1.1: Extract the factor of $17$ from $34i$ to get $\frac{17(2i)}{17i}$.

• Step 1.2: Simplify by removing the shared factors.

  • Step 1.2.1: Recognize that $17i$ also contains the factor $17$, rewriting as $\frac{17(2i)}{17(i)}$.

  • Step 1.2.2: Strike out the $17$ that appears in both numerator and denominator to get $\frac{\cancel{17}(2i)}{\cancel{17}i}$.

  • Step 1.2.3: Present the simplified form of the expression as $\frac{2i}{i}$.

Step 2: Cancel out the common imaginary unit factor.

• Step 2.1: Remove the common $i$ from both numerator and denominator, resulting in $\frac{2\cancel{i}}{\cancel{i}}$.

• Step 2.2: Compute the quotient of $2$ over $1$, which is simply $2$.

Knowledge Notes:

The problem involves simplifying a complex fraction where both the numerator and the denominator contain imaginary units, denoted by $i$. The imaginary unit $i$ is defined as $\sqrt{-1}$.

To solve such problems, one should follow these steps:

1. Identify any common numerical factors between the numerator and the denominator and cancel them out. In this case, both the numerator ($34i$) and the denominator ($17i$) have a common factor of $17$.

2. After canceling the common numerical factors, if both the numerator and the denominator have the imaginary unit $i$, it can also be canceled out since $i/i=1$.

3. Simplify the resulting expression to get the final answer.

In this specific problem, after canceling the common factors, we are left with $2i/i$, which simplifies to $2$ because the imaginary units cancel each other out. The final result is a real number, which is the simplified form of the original complex fraction.