Ask a New Question
Menu

Multiply the complex numbers. Type the answer into the box.

(4-7i)(2+5i) =

1 answer

To multiply the complex numbers \( (4 - 7i)(2 + 5i) \), we can use the distributive property (also known as the FOIL method for binomials).

Let's compute it step by step:

  1. Multiply the real parts: \[ 4 \times 2 = 8 \]

  2. Multiply the outer parts: \[ 4 \times 5i = 20i \]

  3. Multiply the inner parts: \[ -7i \times 2 = -14i \]

  4. Multiply the imaginary parts: \[ -7i \times 5i = -35i^2 \] Since \( i^2 = -1 \), this becomes: \[ -35(-1) = 35 \]

Now, we add all these results together: \[ 8 + 20i - 14i + 35 \]

Combine like terms (real and imaginary):

  1. Real parts: \( 8 + 35 = 43 \)
  2. Imaginary parts: \( 20i - 14i = 6i \)

Putting it all together, we have: \[ 43 + 6i \]

Thus, the product of the complex numbers \( (4 - 7i)(2 + 5i) \) is: \[ \boxed{43 + 6i} \]