(0.5+ 0.2i)^2= 0.5^2- 0.2^2+ (2(0.5)(0.2))i= 0.21+ .2i so (0.5+ 0.2i)+ 2i= 0.21+ 2.2i. You seem to have dropped the hundredths place and that might be important.

If you think of a+ bi as represnting a point, (a, b) in the "complex plane", then it can also be written in polar coordinates with distance from the origin r and angle [itex]\theta[/itex]. Of course, and so But it is also true that [tex]e^{i\theta}= cos(\theta)+ i sin(\theta) so that can be written as . Then , , etc.

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Is that above answer is true?

But I saw in other way like and then bt I couldn't understand this..

Unfortunately, that "polar form" doesn't work well with addition so you would have to change back each time to add the "2i".

In fact, that recursion formula is the one used in calculating Julia sets and the Mandelbrot set so I don't see any method other than 'brute strength" calculation nor do I see that knowing will tell you very much about the limit as n goes to infinity.