5 • Tip for calculating square root of complex no in mind

Mental Calculation, Mathematics, and Puzzles
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I your introduce you to for some things

  1. |z| = it is known as modulo of z
    It is calculated by √(a^2+b^2) in mind
  2. For calculate square root of complex number
    First you calculate |z| and then
    √ \frac{|z| + real part}{2} + i√\frac{|z| - real part}{2}

Example -
Square root of 7 - 24i
|z| = √(7^2 + 24^2) = √(49+ 576) = √625 = 25

√\frac{25+7}{2} - i√\frac{25-7}{2}
= √16 - i√9
= 4 - 3i is the square root.

Example -
Square root of 8+6i
|z| = √(64+36) = √100 = 10
= √\frac{10+8}{2} + i√\frac{10-8}{2}
= √9 + i√1
= 3+ i is the square root.

If you my written text is not clearly I gave you one picture to this

53_1
53_12236×1200 109 KB

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Great formula! First time for me to see this.

I edited the mathematics for readability.

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Wow !!

You deserve a lot of credit for the amount of work on the editing. For me personally, the calculations are much more readable and easier to understand.

As far as the actual maths are concerned, it will take me a few more weeks to arrive at any conclusion - if ever.

An interesting feature of technical editing in industry is that the original text is always left intact. I suppose it’s the same for developers when they use config management on github - only copies of an instance are modified. The original remains intact for the audit trail. Or when the copy explodes, and is discarded. (I’ve forgotten all my config management lingo.)

There’s obviously a whole bunch of maths wizards on this forum who could have checked your edits - but that’s no longer possible.

Maybe @Josh can somehow restore the original post from the site nightly backups - or whatever? Even then, a bit of cut-and-paste might be necessary to link the new to the old.

Just a thought :grin:

Thanks.

. . . . . . .

Added: Just to prove how slowly things occur to me - I should have mentioned that, AFAIK, on other forums a user can’t edit someone else’s post - however good her intentions may be.

Thanks.

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Tank you!

It is true. On Github I can ask for a ‘diff’ and see the changes.

On this forum users cannot edit other users’ posts.
However I am a moderator, so I can :wink:

In general I only edit for readability. I usually do not edit for typo’s nor for grammar. I could edit for rude behaviour but that never happens here.

If I edit, I make it a point of checking the original and the result after my changes. I do not want to remove text from the original post.

Should I have made a mistake and accidentally removed a line or so, then Raja can edit his post or send me a pm to do it.

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5

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Ah yes. Now I remember.

On other forums I’ve seen a note added in a different font, saying something similar to: “Edited by moderator”

Thanks.

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Sorry, I didn’t see your post until now. I get a lot of notifications, and sometimes I miss them.

The edits mainly just added dollar signs around the formulas so that MathJax would format them.

Before:

Square root of 7 - 24i
|z| = √7^2 +24^2 = √49+ 576 = √625 = 25

     √25+7÷2 - i√25- 7÷2
       =     √16 - i√9
       =  (4 - 3i ) is the square root.

After:

Square root of 7 - 24i
|z| = √(7^2 + 24^2) = √(49+ 576) = √625 = 25

√\frac{25+7}{2} - i√\frac{25-7}{2}
= √16 - i√9
= 4 - 3i is the square root.

More info:

1 Like
8

sure, no problem.

9

That’s really impressive!