# Number theory for complex numbers

• ## What is the De Morgan theorem for complex numbers?

De Moivre's theorem gives a formula for computing powers of complex numbers.
We first gain some intuition for de Moivre's theorem by considering what happens when we multiply a complex number by itself.
This shows that by squaring a complex number, the absolute value is squared and the argument is multiplied by 2..

• ## Why do we need number theory?

Number theory is important because of the simple sequence of counting numbers from one to infinity.
Number theory helps to discover interesting relationships between different types of numbers and to prove that they are true.
Number theory is part experimental and part theoretical..

• Results from Number Theory have countless applications in mathematics as well as in practical applications including security, memory management, authentication, coding theory, etc.
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Feb 21, 2019According to the fundamental theorem of algebra, the complex numbers are algebraically closed. This means that any polynomial with complex coefficients can be  What are complex numbers and what is its use in mathematics?What makes number theory so complex? - QuoraWhat is it about complex numbers that yields such amazing theorems?What properties of complex numbers don't work on a set of real More results from www.quora.com
Feb 21, 2019According to the fundamental theorem of algebra, the complex numbers are algebraically closed. This means that any polynomial with complex coefficients can be  What makes number theory so complex? - QuoraWhat are complex numbers and what is its use in mathematics?Why are complex numbers considered to be numbers? - QuoraWhy complex numbers are introduced? - QuoraMore results from www.quora.com
A complex number is just a pair, z = (a, b) of real numbers. We usually write this pair in the form z = a + ib, where the “+” and “i” are just decorations (for now). The number a is called the real part of z, while b is called the imaginary part of z. We denote the set of all complex numbers by C.

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