Asked by Ronald Bourdeau on Jul 06, 2024
Verified
Multiply (−4−−4) ( - 4 - \sqrt { - 4 } ) (−4−−4) by its complex conjugate and simplify.
A) 20
B) 32+32i32 + 32 i32+32i
C) 000
D) 32
E) 8+4i8 + 4 i8+4i
Complex Conjugate
The pair of a complex number, changing the sign of its imaginary part.
Simplify
Making a complex numerical or algebraic expression easier to handle by reducing it to a more basic form.
- Assess the value of expressions that include the complex conjugates of complex numbers.
Verified Answer
ZK
Zybrea KnightJul 09, 2024
Final Answer :
A
Explanation :
The complex conjugate of (−4−−4)(-4 - \sqrt{-4})(−4−−4) is (−4+−4)(-4 + \sqrt{-4})(−4+−4) . Multiplying these together gives (−4−2i)(−4+2i)=16+8i−8i−4=20(-4 - 2i)(-4 + 2i) = 16 + 8i - 8i - 4 = 20(−4−2i)(−4+2i)=16+8i−8i−4=20 .
Learning Objectives
- Assess the value of expressions that include the complex conjugates of complex numbers.