What Determines the Real and Imaginary Parts of a Complex Number?

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Discussion Overview

The discussion centers on the identification and understanding of the real and imaginary parts of complex numbers, specifically in the context of their standard representation as a + ib, where a and b are real numbers. The scope includes conceptual clarification and mathematical reasoning.

Discussion Character

  • Conceptual clarification, Mathematical reasoning

Main Points Raised

  • Some participants assert that in the complex number a + ib, "a" is the real part and "ib" is the imaginary part, with "b" being a real number.
  • Others compare the real and imaginary parts of a complex number to the x and y components of a vector, suggesting that the real part represents the quantity of "ones" and the imaginary part represents the quantity of "i's".
  • It is noted that both the real part and the imaginary part (b) are real numbers.
  • A later reply introduces the idea that complex numbers can also be represented in polar form, adding another layer to the discussion.

Areas of Agreement / Disagreement

Participants generally agree on the identification of "a" as the real part and "b" as the imaginary part of the complex number a + ib. However, the discussion includes varying perspectives on the conceptual understanding of these parts and the introduction of alternative representations, indicating that multiple views remain.

Contextual Notes

The discussion does not resolve potential confusion regarding the terminology of "imaginary" numbers and their interpretation, nor does it address the implications of representing complex numbers in polar form.

Sampad Saha
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we know Complex number is consists of a real & imaginary number so if a+ib is a complex number which one is real part, imaginary part, real number and imaginary number?
I think "a" real and "ib" imaginary part...pleasez help me if Iam wrong ...
 
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Sampad Saha said:
I think "a" real and "ib" imaginary part
As long as you have a and b real, a + ib is the standard representation of a complex number (and, of course, i is the imaginary unit with i2 = -1).
 
the real and imaginary parts of a complex number are like x and y components of a vector.

The real part is the number of "ones" you have, and the imaginary part is the number if "i's" you have

Given a complex number a+bi
ais the real part
and
b is the imaginary part

You have amount a of "ones", and amount b of "i's"
 
jfizzix said:
Given a complex number a+bi
ais the real part
and
b is the imaginary part
It's a little confusing at first, but the real part and the so-called imaginary part b, are real numbers.
 
Just to add that, to be precise, Complex numbers can also be represented in polar form.
 

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