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# I need to know this equation:?

abs(z-3-i)=abs(z+2i)

Thank you!

### 1 Answer

- BrambleLv 79 years agoFavorite Answer
Actually you already know the equation, otherwise you couldn’t have written it. Do you mean you’d like to have someone solve it for z? In that case it would be good manners to say “please” but since you at least say an anticipatory "thank you" and I’m such a helpful and decent person, I shall overlook these shortcomings and derive the answer for you. Meanwhile let me just say that if you are perhaps thinking of entering the engineering profession you would do well to practice clearer communication. It is one of the corner-stones of engineering success that they don't teach you at school!

Let z = a+ib then the given equation becomes:

|a-3 +i(b-1)| = |a + i(b+2)| which means:

(a-3)² + (b-1)² = a² + (b+2)² or a²-6a+9+b²-2b+1 = a²+b² +4b+4 giving:

-6a = 6b -6 or

b = (1 – a)

This represents a line on the Argand diagram. The z value corresponding to any point on the line will satisfy the required condition. E.g set a = 0, then b=1 and the value of z = ib = i.

The LHS of the given equation is then (-3+i0) of which the absolute value = 3

The RHS of the given equation is then (i+i2) = i3 of which the absolute value = 3

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