Roots of Complex Numbers (Sharp, TI, Casio)

[Thomas Klemm]

(12-31-2022 11:58 PM)Matt Agajanian Wrote:  But what function am I using when I put (15625+0.719413999i)^(1/4) into the 42S and get 11+2i as a single result?

Code:

00 { 28-Byte Prgm }
01 RAD
02 POLAR
03 15625
04 0.71941399
05 COMPLEX
06 4
07 1/X
08 Y↑X
09 RECT
10 END

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(12-30-2022 10:58 PM)Matt Agajanian Wrote:  Example Calculate 4th root of (15625+0.719413999i)

Let x= 15625, y=0.719413999

(…)

Example 1: (11 + 2i)^4 = 11753 + 10296i

(Radian Mode)
R>Pr(11,2)^4 sto→ x (15625)
R>PΘ(11,2)*4 sto→ y (0.719413999)

I assume that part of the confusion stems from the fact that you use variables \(x\) and \(y\) for radius and angle.
Thus I suggest to use \(r\) and \(t\) instead.
Hopefully this prevents you from writing \(r + it\) when you mean \(r \cdot e^{it}\).