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
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!!
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).