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the tetration of (1+i) and the (a+bi)^(c+di) formula

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We will find a formula for a complex number raised to a complex power, namely (a+bi)^(c+di)=?
Thanks to Leon M best blader for his email from almost a year ago,    • Complex number to a complex power  

i^i,    • i^i  
Euler's Formula,    • Euler's Formula (but it's a speedrun)  
Math for fun, sin(z)=2,    • Math for fun, sin(z)=2  

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posted by dorkylilmzprzdb