A link from complex number to hypercomplex numbers

[Den Webi]

If i understand correctly, the discovery of complex numbers was linked to solving real number problems, s.a. finding square roots of negative numbers. In other words, at first there was a problem that was formulated using real numbers only that had no real number solutions, which lead to extending the concept of numbers to include complex numbers.

Is there a similar problem that uses complex numbers only but has no complex number solution and requires the introduction of hypercomplex numbers?

Or is it that hypercomplex numbers were discovered/invented by simply adding extra dimensions to complex numbers?

Thank you in advance!

 

[BvU]

Google quaternions or hypercomplex numbers -- but I assume you did that ?

 

[Khashishi]

http://www.askamathematician.com/2012/09/q-is-there-a-number-set-that-is-above-complex-numbers/

 

[Den Webi]

Khashishi, thank you so much, that's exactly what i was looking for!