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sparrow911-Visitor
1-Visitor
Jun 13, 2014 3:17 PM UTC
Question

finding all roots of a complex equation

Hello everyone,

Im trying to find all roots of the equation (2+3i)^(1/4) ...

I can find one in mathcad but have no idea how to make it work out all the others (4 in total) and have had no luck browsing the web so really hope you can help me!

thanks in advance

Konrad

5 replies

Fred_Kohlhepp23-Emerald I
23-Emerald I
Jun 13, 2014 4:19 PM UTC

That's not an equation, that's an imaginary number. Unless you're solving for i; even then there's only i = -0.5

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sparrow911-VisitorAuthor
1-Visitor
Jun 13, 2014 5:41 PM UTC

yes sorry i should have just written the question, rather than explain sorry!.

'simplify the following expression giving the answer in the form a+bi

(2+3i)^(1/4) giving all 4 roots...

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RichardJ19-Tanzanite
19-Tanzanite
Jun 13, 2014 6:53 PM UTC

Use the symbolic processor and the rectangular keyword to rewrite the expression in the form a+bi

To find the roots convert that to the polar form, and use De Moivre's theorum.

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    Werner_E
    Werner_E25-Diamond I
    25-Diamond I
    Jun 13, 2014 9:13 PM UTC

    To get Mathcad to automatically give you all 4 roots you have to symbolically solve the equation z^4=2+3i

    13.06.png

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      sparrow911-VisitorAuthor
      1-Visitor
      Jun 13, 2014 9:26 PM UTC

      Thank you very much Werner.

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