Question

Evaluate the expression (3+5i)-(-3+1i) and write the result in the form a+bi
The real number a equals
The real number b equals

Answer 1

To evaluate the expression \( (3 + 5i) - (-3 + 1i) \), we can simplify it step by step.

1. Distribute the negative sign:
\[
(3 + 5i) - (-3 + 1i) = (3 + 5i) + (3 - 1i)
\]

2. Combine the real parts and the imaginary parts:
- Real parts: \( 3 + 3 = 6 \)
- Imaginary parts: \( 5i - 1i = 4i \)

3. Combine the results:
\[
6 + 4i
\]

So, the result in the form \( a + bi \) is \( 6 + 4i \).

Thus, the values of \( a \) and \( b \) are:
- The real number \( a \) equals \( 6 \).
- The real number \( b \) equals \( 4 \).