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avatar+269 

For what real number k does the product (25+ki)(3+2i) equal a real number?

 Oct 12, 2018

Best Answer 

 #1
avatar+8437 
+3

(25 + ki)(3 + 2i)  =  75 + 50i + 3ki + 2ki2   =   75 + 50i + 3ki - 2k

 

Let's find what value of  k  makes  50i + 3ki  =  0

 

50i + 3ki  =  0

 

i(50 + 3k)  =  0

 

50 + 3k  =  0

 

3k  =  -50

 

k  =  -\(\frac{50}{3}\)

 

When  k  =  -\(\frac{50}{3}\)  ,    (25 + ki)(3 + 2i)   is a real number.

 Oct 12, 2018
 #1
avatar+8437 
+3
Best Answer

(25 + ki)(3 + 2i)  =  75 + 50i + 3ki + 2ki2   =   75 + 50i + 3ki - 2k

 

Let's find what value of  k  makes  50i + 3ki  =  0

 

50i + 3ki  =  0

 

i(50 + 3k)  =  0

 

50 + 3k  =  0

 

3k  =  -50

 

k  =  -\(\frac{50}{3}\)

 

When  k  =  -\(\frac{50}{3}\)  ,    (25 + ki)(3 + 2i)   is a real number.

hectictar Oct 12, 2018
 #2
avatar+269 
+1

Thanks :)

 Oct 12, 2018

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