Questions: Multiply. [ (4+6 i)(8-9 i) ]

Transcript text: Multiply. \[ (4+6 i)(8-9 i) \]

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: \((4+6i)(8-9i) = 4_8 + 4_-9i + 6_8i + 6_-9i^2\).

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

Simplifying the expression, we get: \(ac + adi + bci - bd\) = 32 - 36i + 48i + 54\). Combining like terms, we obtain the complex number: \( 86 + 12i \).

Final Answer:

The product of the complex numbers \((4+6i)\) and \((8-9i)\) is \(86 + 12i\).

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