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This formula basically states that multiplication of complex numbers is related to addition of angles. There is another situation in which multiplication turns into addition, which you may call from your beginning algebra days. Exponent rules have the property that a x a y = a x + y .
Using i as an Exponent - Milefoot
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Using i as an Exponent - Milefoot
www.milefoot.com/math/complex/exponentofi.htm
This formula basically states that multiplication of complex numbers is related to addition of angles. There is another situation in which multiplication turns into addition, which you may call from your beginning algebra days. Exponent rules have the property that a x a y = a x + y . trigonometry - Understanding imaginary exponents - Mathematics ...
https://math.stackexchange.com/questions/9770/understanding-imaginary-exponents
Nov 10, 2010 - Consider a real number A , and take it to the power i . If our system of complex numbers is to be consistent, then A i must be a complex number; in other words, there must be two real numbers x and y , which depend on A , such that: A i = x + i y. Furthermore, we can write A − i = x − i y for the same x and y .
Powers of the imaginary unit (video) | Khan Academy
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And this is the same thing, just from our exponent properties, as i to the fourth power raised to the 25th power ... 
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