What Methods Solve (x+iy)^2 = 5+4i?

  • Thread starter alijan kk
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In summary: I was thinking of the fact that the real and imaginary curves are conjugate and that might help. The solution is just a matter of factoring and applying the quadratic formula. Doing it graphically is just a quick way to see what is happening. A factorable quadratic is quick to solve graphically.In summary, solving for the values of x and y in the equation (x+iy) ^2=5+4i can be done by equating the real and imaginary parts and solving the simultaneous equations. Alternatively, expressing 5+4i in polar form and taking the square root can also provide the solution. The equations can also be solved graphically or by factoring and applying the quadratic formula.
  • #1
alijan kk
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Homework Statement


What is the value of x and y , when (x+iy) ^2=5+4i?

Homework Equations

The Attempt at a Solution


(x+iy)^2=5+4i

x^2+2xiy-y^2=5+4i
 
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  • #2
alijan kk said:

Homework Statement


What is the value of x and y , when (x+iy) ^2=5+4i?

Homework Equations

The Attempt at a Solution


(x+iy)^2=5+4i

x^2+2xiy-y^2=5+4i
Good. Now keep going -- equate the real and imaginary parts and solve the 2 simultaneous equations...
 
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  • #3
alijan kk said:

Homework Statement


What is the value of x and y , when (x+iy) ^2=5+4i?

Homework Equations

The Attempt at a Solution


(x+iy)^2=5+4i

x^2+2xiy-y^2=5+4i

Equate the imagnary and real part. Like if ##x +iy = 3+i5## then I equate to get ##x = 3## and ##y = 5##.
Though there are other ways to take square root of complex numbers.

EDIT :
I did not see post by @berkeman. Sorry don't mean to copy it.
 
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  • #4
The two equations are difficult to solve simultaneously. You can solve graphically for the intercept. Both equations are hyperbolas (one is rotated). Alternatively to solve without graphics you should express 5 + 4i in polar form and then take the square root.
 
  • #5
mpresic said:
The two equations are difficult to solve simultaneously. You can solve graphically for the intercept. Both equations are hyperbolas (one is rotated). Alternatively to solve without graphics you should express 5 + 4i in polar form and then take the square root.

They are not very difficult to solve simultaneously. Using the equation for the imaginary part gives a formula for y in terms of x. Then substituting that formula into the equation for the real part gives a quadratic equation in x2, which is easily solved using standard formulas.
 
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  • #6
Yes, That is interesting. Expressing in polar form and taking square root is OK too.
 

Related to What Methods Solve (x+iy)^2 = 5+4i?

1. What is the process for solving equations?

The process for solving equations involves isolating the variable on one side of the equation and simplifying the other side until you reach a solution. This usually involves using inverse operations, such as addition and subtraction or multiplication and division, to cancel out any coefficients or constants on the variable.

2. How do I know which operation to use when solving equations?

The operation you use when solving equations depends on the type of equation you are working with. For linear equations, you will typically use addition and subtraction to isolate the variable. For quadratic equations, you may need to use factoring or the quadratic formula. It is important to carefully analyze the equation and determine the best approach to solving it.

3. What do I do if there are variables on both sides of the equation?

If there are variables on both sides of the equation, the first step is to combine like terms on both sides. Then, use inverse operations to isolate the variable on one side of the equation. Once the variable is isolated, continue to simplify the other side until you reach a solution.

4. Can I check my solution to an equation?

Yes, it is always a good idea to check your solution to an equation. To check, simply substitute the solution into the original equation and simplify both sides. If the two sides are equal, then your solution is correct.

5. What should I do if I get stuck when solving an equation?

If you get stuck when solving an equation, take a step back and review the process. Make sure you have correctly applied inverse operations and simplified both sides of the equation. You can also try plugging in different values for the variable to see if you can find a solution. If you still cannot solve the equation, reach out to a teacher or tutor for assistance.

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