Use app×
Join Bloom Tuition
One on One Online Tuition
JEE MAIN 2025 Foundation Course
NEET 2025 Foundation Course
CLASS 12 FOUNDATION COURSE
CLASS 10 FOUNDATION COURSE
CLASS 9 FOUNDATION COURSE
CLASS 8 FOUNDATION COURSE
0 votes
165 views
in Complex Numbers by (20 points)
Q 1. Find the value of \( 2 x^{3}-11 x^{2}+44 x+27 \), if \( x=\frac{25}{3-4 i} \) (without direct substitution)

Please log in or register to answer this question.

1 Answer

0 votes
by (20 points)

\(x = \frac{25}{3+4i}\\ x=25\frac{(3-4i)}{(3+4i)(3-4i)} \\x = 25\frac{(3-4i)}{9+16}\\ x=3-4i\)

x = 3-4i

\(x^2 = (3-4i)^2 = (3)^2 + (4i)^2 -(2)(3)(4i)\\ = 9 -16 -24i = -7 - 24i\\x^2 = -7-24i\)

\(x^3 = x^2\times x = (-7-24i)(3-4i) = -21 + 28i - 72i + (24i\times4i)\\ \Rightarrow-44i-21-96 = -44i-117\)

\(2,-11,44,27\\ 2(-44i-117) -11(-7-24i) + 44 (3-4i) + 27\\ \Rightarrow -88i -334 + 77 + 264i +132 - 176i + 27\\ \Rightarrow 264i -88i - 176i +132+77+27 - 334 \Rightarrow 0i +226-334 = -108\)

Answer = -108

No related questions found

Welcome to Sarthaks eConnect: A unique platform where students can interact with teachers/experts/students to get solutions to their queries. Students (upto class 10+2) preparing for All Government Exams, CBSE Board Exam, ICSE Board Exam, State Board Exam, JEE (Mains+Advance) and NEET can ask questions from any subject and get quick answers by subject teachers/ experts/mentors/students.

...