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

In summary, the question is asking for all possible solutions for the complex number z, which can be represented as z= x+ iy. The solution involves using De Moivre's formula and equating the real and imaginary parts of z^2= a+ bi. This question is meant to develop problem-solving skills and can be approached by using the homework template.
  • #1
kat1812
3
0
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.
 
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  • #2
kat1812 said:
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!
 
Last edited:
  • #3
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.
 
  • #4
epenguin said:
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 said:
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 :)
 

1. What are complex numbers?

Complex numbers are numbers that have both a real and imaginary component. They are typically written in the form a + bi, where a is the real part and bi is the imaginary part with i being the imaginary unit (√-1).

2. How are complex numbers used in math and science?

Complex numbers are used in a variety of mathematical and scientific applications, such as solving polynomial equations, representing alternating currents in electrical engineering, and analyzing quantum mechanics and signal processing.

3. What is the difference between a real number and a complex number?

A real number is any number that can be plotted on a number line, including both positive and negative numbers. A complex number, on the other hand, includes both a real and imaginary component and cannot be plotted on a number line.

4. How do you add and subtract complex numbers?

To add or subtract complex numbers, you simply combine the real parts and the imaginary parts separately. For example, (3 + 2i) + (5 + 4i) = (3 + 5) + (2i + 4i) = 8 + 6i. To subtract, you follow the same process but use subtraction instead of addition.

5. Can complex numbers have a magnitude and direction like vectors?

Yes, complex numbers can be represented as vectors in the complex plane. The magnitude of a complex number is its distance from the origin, and the direction is the angle it makes with the positive real axis. This representation is often used in polar form, where a complex number is written as r(cosθ + isinθ) with r as the magnitude and θ as the direction.

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