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

Question

asked Aug 20, 2022 55.7k views

1 Answer

Teddy Koker · Answer 1 · 2022-08-26T04:48:35+0000

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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

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