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For complex number z, what is 2z + i = iz + 3?

(Please respond in form x + yi)

 

Thanks for your time!

 Nov 28, 2019
 #1
avatar+105476 
+1

2z  + i   =  iz +  3

 

2 (a + bi)  + i   =  i ( a + bi) + 3

 

2a + 2bi + 1i  =  ai - b + 3

 

Equating real and complex parts

 

2a  = 3 - b     ⇒    2a + b  = 3    ⇒  4a + 2b  = 6    (1)

(2b + 1)  =  a ⇒     a - 2b =  1   ⇒    a  - 2b  =  1      (2)

 

Add (1)  and (2)  and we get that

 

5a = 7

a = 7/5

 

And

2(7/5) + b  = 3

14/5 + b = 15/5

b = 15/5 - 14/5

b = 1/5

 

So

 

z = a + bi

 

z  = (7/5)  + (1/5) i

 

 

cool cool cool

 Nov 28, 2019

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