Roots of Complex Numbers (Sharp, TI, Casio)

[Matt Agajanian]

(01-02-2023 08:47 AM)Thomas Klemm Wrote:  

(01-01-2023 10:03 PM)Matt Agajanian Wrote:  Correct?

This looks good to me.
But now both blocks became identical.

You could use variables \(x\) and \(y\) instead of \(a\) and \(b\) if that helps for readability.
And another variable \(n\) for the exponent instead of \(4\):

R>Pr(x, y)^n sto r
R>PΘ(x, y)*n sto t
P>Rx(r, t)
P>Ry(r, t)

Now you can use it for any of these cases:

• \(n = 4\)
• \(n = -4\)
• \(n = \frac{1}{4}\)
  

Excellent techniques

I’ve been working on some new routines.

Please let me know if any of these are legit:

Even if you're not familiar with the TI 36X Pro or 30X MathPrint, the keystrokes should be self-explanatory.

Complex Number Power & Root Calculations
(x+yi)^n
Example: (11+2i)^4
R→Pr(11,2)^4 (15625)
sto x
R→Pθ(11,2)*4 (0.719413999)
sto y
P→Rx(x,y) 11753
P→Ry(x,y) 10296

Fourth root of r∡θ [(r∡θ)^1/4]
Example: (15625∡ 0.719413999)^1/4
15625^1/4 11.18033989
sto x
0.719413999/4 0.17985335
sto y
P→Rx(x,y) 11
P-Ry(x,y) 2

Fourth root of (x+yi) [(x+yi)^1/4]
Example: (11753+10296 i)^1/4
11753
sto x
10296
sto y
R→Pr(x,y)^.25
sto a
R→Pθ(x,y)/4
sto b
P→Rx(a,b) 11
P→Ry(a,b) 2

(r∡θ)^n
Example: (11.18033989∡0.1798535)^4 (11+2i)^4 in polar form)
(11.18033989∡0.1798535)^4
11.18033989
sto x
0.1798535
sto y
P→Rx(x^4,y*4) → 11753
sto a
P→Ry(x^4,y*4) → 10296
sto b
R→Pr(a,b) → 15625
R→Pθ(a,b) → 0.71914

Thanks