객관식
Multiply the following and simplify.
93
views
9. Roots, Radicals, and Complex Numbers
Multiplying and Dividing Complex Numbers
Multiple Choice
Find the product of the given complex number and its conjugate.
A
B
C
D
검증된 단계별 안내1
Identify the given complex number as \(-7 - i\) and its conjugate as \(-7 + i\). The conjugate of a complex number \(a + bi\) is \(a - bi\).
Set up the product of the complex number and its conjugate: \((-7 - i)(-7 + i)\).
Use the distributive property (FOIL method) to expand the product: \((-7)(-7) + (-7)(i) + (-i)(-7) + (-i)(i)\).
Simplify each term: \(49 - 7i + 7i - i^2\). Notice that \(-7i\) and \(+7i\) cancel each other out.
Recall that \(i^2 = -1\), so replace \(-i^2\) with \(-(-1) = +1\). Then add the remaining terms: \(49 + 1\).
Related Videos
Related Practice