# Complex Number

A complex number is a number that can be put in the form a + bi, where a and b are real numbers and i is called the imaginary unit, where i2 = −1. In this expression, a is called the real part and b the imaginary part of the complex number. Complex numbers extend the idea of the one-dimensional number line to the two-dimensional complex plane by using the horizontal axis for the real part and the vertical axis for the imaginary part. The complex number a + bi can be identified with the point (a, b). A complex number whose real part is zero is said to be purely imaginary, whereas a complex number whose imaginary part is zero is a real number. In this way the complex numbers contain the ordinary real numbers while extending them in order to solve problems that cannot be solved with only real numbers.

Complex numbers are used in many scientific fields, including engineering, electromagnetism, quantum physics, and applied mathematics, such as chaos theory. Italian mathematician Gerolamo Cardano is the first known to have introduced complex numbers. He called them "fictitious", during his attempts to find solutions to cubic equations in the 16th century.

Read more about Complex Number:  Overview, Complex Analysis, History, Generalizations and Related Notions

### Other articles related to "complex number, complex numbers, complex, numbers, number":

Complex Number - Generalizations and Related Notions
... dimension, the algebraic properties familiar from real and complex numbers vanish the quaternions are only a skew field, i.e ... following the R-linear map for some fixed complex number w can be represented by a 2×2 matrix (once a basis has been chosen) ... the one mentioned in the section on matrix representation of complex numbers above ...
Complex Conjugate
... In mathematics, complex conjugates are a pair of complex numbers, both having the same real part, but with imaginary parts of equal magnitude and ... For example, 3 + 4i and 3 − 4i are complex conjugates ... The conjugate of the complex number where and are real numbers, is For example, An alternative notation for the complex conjugate is ...
Logrithm - Generalizations - Complex Logarithm
... The complex numbers a solving the equation are called complex logarithms ... Here, z is a complex number ... A complex number is commonly represented as z = x + iy, where x and y are real numbers and i is the imaginary unit ...
Difference Of Two Squares - Uses - Complex Number Case: Sum of Two Squares
... used to find the linear factors of the sum of two squares, using complex number coefficients ... Since the two factors found by this method are Complex conjugates, we can use this in reverse as a method of multiplying a complex number to get a real number ... This is used to get real denominators in complex fractions ...
Laguerre's Method - Derivation
... becomes Solving these equations, we find that , where the square root of a complex number is chosen to produce larger absolute value of the denominator, or equivalently ... by adding a suitable complex number to give distinct roots distinct magnitudes if necessary (which it will be if some roots are complex conjugates), and then repeatedly applying the root ...

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