Complex numbers (5+2i)=SQRT(x+iy)

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Discussion Overview

The discussion revolves around solving the equation (5+2i)=SQRT(x+iy), focusing on methods for evaluation, including algebraic manipulation and polar form representation. Participants explore different approaches to find the values of x and y.

Discussion Character

  • Exploratory, Technical explanation, Mathematical reasoning

Main Points Raised

  • One participant suggests raising both sides to the power of 2 or converting to polar form as potential methods for solving the equation.
  • Another participant notes that squaring both sides leads to the equation 21 = x + iy, which raises questions about the imaginary part of the solution.
  • A participant corrects a misunderstanding regarding the squaring of complex numbers, emphasizing that (5 + 2i)^2 is not simply 5^2 + (2i)^2, and provides a detailed expansion of the expression.
  • One participant expresses gratitude for the clarification and mentions that the polar form approach also yields satisfactory results.

Areas of Agreement / Disagreement

Participants do not reach a consensus on the best method for solving the equation, as different approaches are discussed and some misunderstandings are corrected.

Contextual Notes

There are unresolved aspects regarding the interpretation of the imaginary part in the context of the equation, and the discussion reflects varying levels of familiarity with complex number operations.

Who May Find This Useful

Readers interested in complex numbers, mathematical problem-solving techniques, and the evaluation of equations involving imaginary components may find this discussion relevant.

johnwalton84
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How do you evaluate this type of problem:

(5+2i)=SQRT(x+iy)
 
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Have you considered raising both sides to the power of 2? Or writing both sides in polar form?
 
Last edited:
Yes, but when you do that the i value on the left disappears and you get

21 = x+iy

which suggests that there is no imaginary part of the solution (?)


I haven't tried writing both sides in polar form, i'll try that now
 
Yes, but when you do that the i value on the left disappears and you get

21 = x+iy

No, since (5 + 2i)^2 is NOT equal to 5^2 + (2i)^2.

(5 + 2i)^2 = (5 + 2i)(5 + 2i) = 5*5 + 5*2i + 2i*5 + 2i*2i = 25 + 10i + 10i - 4, etc.
 
:blushing: of course :blushing:

:smile: thanks

it works fine in polars as well
 

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