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Solve 2z+i=iz+3  Express your answer in the form: x+yi

 Apr 24, 2023
 #1
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We can solve this equation by subtracting iz+3 from both sides, which gives us:

2z - iz = 3

Combining like terms, we get:

z(2 - i) = 3

Dividing both sides by 2−i, we get:

z = 3 / (2 - i)

We can simplify this expression by multiplying the numerator and denominator by the conjugate of the denominator, which is 2+i. This gives us:

z = 3(2 + i) / (2^2 - (-1)) = 3(2 + i) / 5 = (6 + 3i) / 5 = 6/5 + 3/5*i.

 Apr 24, 2023
 #2
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\(2z+i = iz+3\\ z(2-i)=3-i\\z=\frac{3-i}{2-i}\\z=\frac{3-i}{2-i}\times\frac{2+i}{2+i}\\z=\frac{(3-i)(2+i)}{2^2-i^2}\)

 

Can you take it from here?

 Apr 24, 2023

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