# Express z in the form a+ib

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1. Apr 29, 2017

### CheesyPeeps

1. The problem statement, all variables and given/known data
I've used z* to mean z conjugate.
Given the equation z + 2iz* = 8 + 7i, express z in the form a + ib.

From SQA Advanced Higher Mathematics 2005 Exam Paper
2. Relevant equations
n/a

3. The attempt at a solution
I substituted a+ib and its conjugate in for z and z*, which, after some rearranging, gave me z =-3-15i.
I am not sure if that's the correct answer, and I'm a bit suspicious of how straightforward that method was. The question is worth 4 marks, which seems an awful lot for not much work. Have I missed something?

2. Apr 29, 2017

### Buzz Bloom

Hi CheezePeeps:

I got a different answer than you did. I agree the problem is straight forward, but careless mistakes are possible. Please post the details of how you arrived at your answer?

Regards,
Buzz

3. Apr 29, 2017

### CheesyPeeps

I looked back over my initial working, and there were definitely some careless mistakes made from rushing through the steps too quickly!
I redid the problem, making sure that I didn't cut any corners or make arithmetic errors, and I got z = 2 + 3i.
To get z = 2 + 3i, I equated the real and imaginary parts of the equation after substituting in a+ib and a-ib, then used simultaneous equations to get the values of a and b.

4. Apr 29, 2017

### Buzz Bloom

Hi CheezePeeps:

That is the answer I got.

Regards,
Buzz

5. Apr 29, 2017

### Ray Vickson

One strategy that you should always use is to check your answer by substituting it into the original equation to see if it "works". In an exam setting that is all you can do: no appeal to outside help.