I assume you are using the * to represent conjugate. You should know that , so we have and . Subtracting the second equation from the first gives

So the solution is or

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- September 17th 2012, 08:13 PM #1

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## Please help me!! >.<

Please teach me how to solve this question...

Two complex number w and z are such that w*= z -2i and |w|^2=z+6. By eliminating z, find w in the form a+ib, where a and b are real and positive.

please help me! I really have many problems with complex number!!

- September 17th 2012, 09:02 PM #2

- September 17th 2012, 09:13 PM #3

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## Re: Please help me!! >.<

Are you sure you copied the problem correctly?

Assuming you did:

1. What does |w|^2=z+6 say about the complex number z? (Hint: what kind of values can |w| take?)

2. Do you know "eliminate z" algebraically? (If not, then that kind of algebra is something you should heavily review - it's very important.)

3. Just so you can see how you're doing - it's eventually a quadratic you'll need to solve, and so you'll have two solutions for w. And they'll be clean, like (integer) + i(integer).