Asked by Melanie Mclean on May 15, 2024
Verified
Multiply (2+8i) ( 2 + 8 i ) (2+8i) by its complex conjugate and simplify.
A) 68
B) −60- 60−60
C) 10+8i10 + 8 i10+8i
D) 68+32i68 + 32 i68+32i
E) 10
Complex Conjugate
The complex conjugate of a complex number is the number with an equal real part and an imaginary part equal in magnitude but opposite in sign.
Simplify
The process of altering an expression to make it easier to understand or work with, often by reducing its complexity.
- Evaluate expressions involving complex conjugates of complex numbers.
Verified Answer
DS
David SantiagoMay 19, 2024
Final Answer :
A
Explanation :
The complex conjugate of 2+8i2 + 8i2+8i is 2−8i2 - 8i2−8i . Multiplying these together: (2+8i)(2−8i)=4−64i2(2 + 8i)(2 - 8i) = 4 - 64i^2(2+8i)(2−8i)=4−64i2 . Since i2=−1i^2 = -1i2=−1 , this simplifies to 4+64=684 + 64 = 684+64=68 .
Learning Objectives
- Evaluate expressions involving complex conjugates of complex numbers.