The product of two numbers is 41. One of the numbers is the complex number 5+4i. What is the other
number?

A. 5-4i
B. 5+4i
C. -5-4i
D. -5+4i
E. 41/5-4i

Work Shown:

x = the other number

(5+4i)*x = 41

x = 41/(5+4i)

x = 41*(5-4i)/( (5+4i)*(5-4i) ) see note below

x = 41*(5-4i)/( 41 )

x = (41/41)*(5-4i)

x = 5 - 4i  

As a way to check, (5+4i)*(5-4i) = 5^2+4^2 = 25+16 = 41

The rule used is (a-bi)(a+bi) = a^2 + b^2

Note:  I multiplied top and bottom by (5-4i) to get rid of the imaginary term in the denominator.

sorry i just need to anwers this to get points

step-by-step explanation:

3

step-by-step explanation: