Question

Question 5 options:
Multiply (2−5i)(3+i)

Answer 1

To multiply the complex numbers \((2−5i)(3+i)\), we can use the distributive property (also known as the FOIL method for binomials).

1. **First:** Multiply the first terms:
\[
2 \cdot 3 = 6
\]

2. **Outer:** Multiply the outer terms:
\[
2 \cdot i = 2i
\]

3. **Inner:** Multiply the inner terms:
\[
-5i \cdot 3 = -15i
\]

4. **Last:** Multiply the last terms:
\[
-5i \cdot i = -5i^2
\]

Since \(i^2 = -1\), we have:
\[
-5i^2 = -5(-1) = 5
\]

Now, combine all these results together:
\[
6 + 2i - 15i + 5
\]
Combine the real parts and the imaginary parts:
\[
(6 + 5) + (2i - 15i) = 11 - 13i
\]

So, the final result is:
\[
\boxed{11 - 13i}
\]