SOLUTION: For which of the following operations will the complex numbers (4-3i) and (1+2i) produce a real solution? Find the solution. A) Addition B) Subtraction C) Multiplication D) D

Algebra ->  Complex Numbers Imaginary Numbers Solvers and Lesson -> SOLUTION: For which of the following operations will the complex numbers (4-3i) and (1+2i) produce a real solution? Find the solution. A) Addition B) Subtraction C) Multiplication D) D      Log On


   

Question 1065588: For which of the following operations will the complex numbers (4-3i) and (1+2i) produce a real solution? Find the solution.
A) Addition
B) Subtraction
C) Multiplication
D) Division

Thanks!
Answer by josgarithmetic(39620) About Me  (Show Source):
You can put this solution on YOUR website!
If you are not sure, try each of them and see.

Addition will give you an imaginary component, and so will subtraction.

Multiplication?
4-3i%2B2i-6i%5E2
No. You have the imaginary, -i as part of the number.

Division?
-
%284-3i%29%2F%281%2B2i%29
%28%284-3i%29%2F%281%2B2i%29%29%28%281-2i%29%2F%281-2i%29%29, simply multiplication by 1
%284-3i-8i%2B6i%5E2%29%2F%281-4i%5E2%29------but you still will have an imaginary component in the numerator.
-
You can also try the reciprocal and see what it will be, but...
You try it.
Unless this gives you a fully REAL result, none of the choices will produce a real solution.