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- DictionaryCom·plex
adjective
- 1. consisting of many different and connected parts: "a complex network of water channels"
- 2. denoting or involving numbers or quantities containing both a real and an imaginary part.
noun
- 1. a group of similar buildings or facilities on the same site: "a new apartment complex"
- 2. a related group of emotionally significant ideas that are completely or partly repressed and that cause psychic conflict leading to abnormal mental states or behavior.
verb
- 1. make (an atom or compound) form a complex with another: "the DNA was complexed with the nuclear extract"
2 days ago · If G is a suitable group endowed with a measure λ, and if f and g are real or complex valued integrable functions on G, then we can define their convolution by ( f ∗ g ) ( x ) = ∫ G f ( y ) g ( y − 1 x ) d λ ( y ) . {\displaystyle (f*g)(x)=\int _{G}f(y)g\left(y^{-1}x\right)\,d\lambda (y).}
5 days ago · The field of complex numbers, denoted by ℂ, is the set of all ordered pairs of real numbers together with the following arithmetic operations. Addition: z ₁ + z ₂ = ( x ₁ + y ₁ j) + ( x ₂ + y ₂ j) = x ₁ + x ₂ + j ( y ₁ + y ₂). Substraction: z ₁ − z ₂ = ( x ₁ + y ₁ j) − ( x ₂ + y ₂ j) = x ₁ − x ₂ + j ...
3 days ago · In mathematics, the quaternion number system extends the complex numbers. Quaternions were first described by the Irish mathematician William Rowan Hamilton in 1843 and applied to mechanics in three-dimensional space. The algebra of quaternions is often denoted by H (for Hamilton), or in blackboard bold by .
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6 days ago · Modern definitions express trigonometric functions as infinite series or as solutions of differential equations. This allows extending the domain of sine and cosine functions to the whole complex plane, and the domain of the other trigonometric functions to the complex plane with some isolated points removed.
4 days ago · Complex roots are special types of solutions to equations that appear as complex numbers, particularly when dealing with quadratic equations whose discriminant is negative. These roots consist of a real part and an imaginary part, represented as α = a + ib and β = c + id, where “i” is the square root of -1.
5 days ago · Streptomyces umbrella toxin particles block hyphal growth of competing species. Streptomyces are discovered to produce antibacterial protein complexes that selectively inhibit the hyphal growth of ...
5 days ago · One can define vectors using Mathematica commands: List, Table, Array, or curly brackets. In mathematics and applications, it is a custom to distinguish column vectors \[ {\bf v} = \left( \begin{array}{c} v_1 \\ v_2 \\ \vdots \\ v_m \end{array} \right) \qquad \mbox{also written as } \qquad {\bf v} = \left[ \begin{array}{c} v_1 \\ v_2 \\ \vdots ...
