Multiple Choice
Find the product. Express your answer in standard form.
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11. Roots, Radicals, and Complex Numbers
Multiplying and Dividing Complex Numbers
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Find the product of the given complex number and its conjugate.
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Verified step by step guidance1
Identify the given complex number as \$4 - 5i\( and its conjugate as \)4 + 5i\(. The conjugate of a complex number \)a + bi\( is \)a - bi$.
Set up the product of the complex number and its conjugate: \((4 - 5i)(4 + 5i)\).
Use the distributive property (FOIL method) to expand the product: multiply the first terms, outer terms, inner terms, and last terms.
Recall that \(i^2 = -1\), so simplify the terms involving \(i^2\) accordingly.
Combine like terms (real parts and imaginary parts) to write the product as a real number.
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