Multiply the complex numbers (4−5i) and (3−2i). Express the answer in the form x+iy.

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here's the solution for problem 6. Step 1: Write the given expression. We need to multiply the complex numbers (4−5i) and (3−2i). (4−5i)(3−2i) Step 2: Expand the product using the distributive property (FOIL method). Multiply each term in the first parenthesis by each term in the second parenthesis: 4(3) + 4(−2i) − 5i(3) − 5i(−2i) 12 − 8i − 15i + 10i² Step 3: Substitute i² = −1. 12 − 8i − 15i + 10(−1) 12 − 8i − 15i − 10 Step 4: Combine the real parts and the imaginary parts. Group the real terms and the imaginary terms: (12 − 10) + (−8i − 15i) 2 − 23i The expression in the form x+iy is 2−23i. The final answer is 2−23i.

Multiply the complex numbers (4-5i) and (3-2i). Express the answer in the form x+iy.

Answer

Step-by-step solution

Write the given expression.

Expand the product using the distributive property (FOIL method).

Substitute $i^2 = -1$ .

Combine the real parts and the imaginary parts.

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