sankarshana016 said:Taking a=cosθ+isinθ, but didn't get anywhere
Do you know the factorization of ##\ a^3+1\ ?##sankarshana016 said:If a is a complex number, and a^2-a+1=0, then a^2011=?
I tried using De Moivre's theorem, Taking a=cosθ+isinθ, but didn't get anywhere, got stuck at
cos2θ+isin2θ-cosθ-isinθ+1=0. What do I do?
SammyS said:Do you know the factorization of ##\ a^3+1\ ?##
sankarshana016 said:If a is a complex number, and a^2-a+1=0, then a^2011=?
I tried using De Moivre's theorem, Taking a=cosθ+isinθ, but didn't get anywhere, got stuck at
cos2θ+isin2θ-cosθ-isinθ+1=0. What do I do?
Complex numbers are numbers that consist of both a real and an imaginary part. They are written in the form a + bi, where a is the real part and bi is the imaginary part, with i being the imaginary unit equal to the square root of -1.
Complex numbers are used in many areas of mathematics, including algebra, geometry, and calculus. They are particularly useful in solving problems involving electrical circuits, quantum mechanics, and fluid dynamics.
A real number is any number that can be represented on the number line, including all positive and negative integers, fractions, and decimals. A complex number, on the other hand, includes both a real and imaginary part and cannot be represented on a number line.
To add or subtract complex numbers, you simply combine the real parts and the imaginary parts separately. For example, to add (3 + 2i) and (5 - 4i), you add 3 and 5 to get 8, and add 2i and -4i to get -2i, giving you a final answer of 8 - 2i.
Yes, complex numbers can have exponents. To raise a complex number to a power, you can use the expression (a + bi)^n = (a^n + nb^(n-1)i + ... + nbi^(n-1)). This is known as de Moivre's formula.