Questions: Multiply. (3-5i)(4-6i)

Transcript text: Multiply. \[ (3-5 i)(4-6 i) \]

Solution

Solution Steps

Step 1: Apply the distributive property (FOIL method)

Using the FOIL method, we multiply the complex numbers as follows: \((a+bi)(c+di) = ac + adi + bci + bdi^2\). Substituting the given values, we get: \((3-5i)(4-6i) = 3_4 + 3_-6i - 5_4i - 5_-6i^2\).

Step 2: Simplify the expression by combining like terms and using the fact that \(i^2 = -1\)

Simplifying the expression, we get: \(ac + adi + bci - bd\) = 12 - 18i - 20i - 30\). Combining like terms, we obtain the complex number: \( -18 - 38i \).

Final Answer

The product of the complex numbers \((3-5i)\) and \((4-6i)\) is \(-18 - 38i\).

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