2025 AMC 12B Problem 3Problem 3 of 25·Easier·AlgebraWhat is the value of i(i−1)(i−2)(i−3),i(i-1)(i-2)(i-3),i(i−1)(i−2)(i−3), where i=−1?i = \sqrt{-1}?i=−1?Answer choicesA6−5i6 - 5i6−5i1B−10i-10i−10i2C10i10i10i3D−10-10−104E1010105Submit answerStuck? Show hintsShow solutionSolutioni(i−1)=i2−i=−1−i,i(i-1) = i^2 - i = -1 - i,i(i−1)=i2−i=−1−i, and (i−2)(i−3)=i2−5i+6(i-2)(i-3) = i^2 - 5i + 6(i−2)(i−3)=i2−5i+6 =5−5i.= 5 - 5i.=5−5i. Then (−1−i)(5−5i)=−5+5i−5i+5i2=−5−5=−10. \begin{gathered} (-1-i)(5-5i) = -5 \\ {}+ 5i - 5i \\ {}+ 5i^2 \\ = -5 - 5 = -10. \end{gathered} (−1−i)(5−5i)=−5+5i−5i+5i2=−5−5=−10. Thus, the correct answer is D.AoPS wikiCopy problemTagged: complex number