Thread: Complex Number

Can help me to solve this?

1. Given that , find the values of p and q when p and q are respectively a complex number and its conjugate.

2. Given that the complex number z and its conjugate z* satisfy the equation , find the possible values of z.

3. Given that z=x+yi and . If w is totally imaginary, show that .


Answers:

1. p=2-i, q=2+i
2. 3-i, 3+3i

Originally Posted by cloud5

3. Given that z=x+yi and . If w is totally imaginary, show that .

We solved a problem like this one in this thread: http://www.mathhelpforum.com/math-he...ex-number.html


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Going a bit backwards here:

Originally Posted by cloud5

2. Given that the complex number z and its conjugate z* satisfy the equation , find the possible values of z.

If , then :



Now equate the real and imaginary coefficients:


So the answers, in the form of a + bi, are
3 + 3i and
3 - i.

Originally Posted by cloud5

1. Given that , find the values of p and q when p and q are respectively a complex number and its conjugate.

This looks like the same problem as #2. Substitute a + bi for p and a - bi for q. Set the real and imaginary coefficients equal to each other and solve for a and b.


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