Simply to a + bi: - 2 / (3 - 1) * (5 / i) =
Understand the Problem
The question is asking to simplify the expression
- \frac{2}{3-1} \left( \frac{5}{i} \right). This involves simplifying the fraction and dealing with the imaginary unit i.
Answer
The simplified expression is \( -5i \).
Answer for screen readers
The simplified expression is ( -5i ).
Steps to Solve
- Simplify the denominator
First, simplify the expression in the denominator: $$ 3 - 1 = 2 $$
- Rewrite the expression
Now, substitute the simplified denominator back into the expression: $$ \frac{2}{2} \left( \frac{5}{i} \right) $$
- Simplify the fraction
Next, simplify the fraction: $$ \frac{2}{2} = 1 $$ So, we have: $$ 1 \left( \frac{5}{i} \right) $$
- Multiply by the reciprocal of ( i )
To eliminate ( i ) from the denominator, multiply by ( \frac{-i}{-i} ): $$ \frac{5}{i} \times \frac{-i}{-i} = \frac{-5i}{-i^2} $$
- Substitute ( i^2 )
Since ( i^2 = -1 ), replace it: $$ -i^2 = 1 $$ So, the expression now is: $$ \frac{-5i}{1} = -5i $$
The simplified expression is ( -5i ).
More Information
The expression simplifies to a purely imaginary number. The use of ( i ), the imaginary unit, is critical in computations involving complex numbers, where ( i^2 ) equals (-1).
Tips
- Forgetting to rationalize the denominator when dealing with ( i ).
- Neglecting to simplify fractions completely before proceeding to multiplication.
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