Possible solutions for z: √(a+bi) or -√(a+bi)

[kat1812]

Hello!

I am very unsure of how to solve this question.

The question states z^2=a+bi, where a and b belong to real numbers. Find all possible solutions for z. I think that the solution includes the De Moivre's formula, however I am very confused by how to do this or what the formula means.
Thanks in advance for any help.

 

[epenguin]

Hello!

I am very unsure of how to solve this question.

The question states z^2=a+bi, where a and b belong to real numbers. Find all possible solutions for z. I think that the solution includes the De Moivre's formula, however I am very confused by how to do this or what the formula means.
Thanks in advance for any help.

Welcome to the Forum!

For one thing you could say to yourself: z is also a complex number.

Write that fact down - as an equation using your own symbols.

Think what you could do with the two formulae you then have.

You are being asked in order to give you the habit of knowing what to do faced with such a question.

Perhaps using the homework template would have suggested or forced you to make a step in that direction!

 

[HallsofIvy]

Write z= x+ iy. Now replace z with that in z^2= a+ bi. Do the actual multiplication on the left and equate real and imaginary parts.

 

[kat1812]

Welcome to the Forum!

For one thing you could say to yourself: z is also a complex number.

Write that fact down - as an equation using your own symbols.

Think what you could do with the two formulae you then have.

You are being asked in order to give you the habit of knowing what to do faced with such a question.

Perhaps using the homework template would have suggested or forced you to make a step in that direction!

Write z= x+ iy. Now replace z with that in z^2= a+ bi. Do the actual multiplication on the left and equate real and imaginary parts.

Thank you to both of you! I will try and give this a go :)