Scelta multipla
Find the product. Express your answer in standard form.
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9. Roots, Radicals, and Complex Numbers
Multiplying and Dividing Complex Numbers
Scelta multipla
Find the product of the given complex number and its conjugate.
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Guida verificata passo dopo passo1
Identify the given complex number, which is \(4 - 5i\), and write down its conjugate. The conjugate of a complex number $a + bi$ is $a - bi$, so the conjugate of \(4 - 5i\) is \(4 + 5i\).
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 when you multiply the imaginary parts, replace \(i^2\) with \(-1\) to simplify the expression.
Combine like terms (real parts and imaginary parts) to get the final simplified product, which will be a real number.
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