complex number (english) - meaning, definition, translation, pronunciation

Part of Speech

Noun

Phonetic Transcription

/ˈkɒmplɛks ˈnʌmbər/

Meaning and Usage

A complex number is a number that can be expressed in the form ( a + bi ), where ( a ) and ( b ) are real numbers, and ( i ) is the imaginary unit, which satisfies the equation ( i^2 = -1 ). The part ( a ) is called the real part, and ( bi ) is the imaginary part. Complex numbers are widely used in various fields such as engineering, physics, and applied mathematics to solve equations that cannot be resolved using only real numbers.

In terms of frequency of use, complex number is used more frequently in written contexts, especially in academic, technical, or scientific discussions.

Example Sentences

1. The solution to the equation was a complex number.

2. La solución de la ecuación era un número complejo.

3. Complex numbers are essential in the study of electrical engineering.

4. Los números complejos son esenciales en el estudio de la ingeniería eléctrica.

5. In advanced mathematics, understanding complex numbers is crucial.

6. En matemáticas avanzadas, entender los números complejos es crucial.

Idiomatic Expressions

The term "complex number" itself does not typically feature in idiomatic expressions, as it is a mathematical term. However, there are various phrases associated with "complex" that may convey the multifaceted nature of situations or problems.

Example Sentences with Related Idiomatic Expressions

1. "The issue at hand is quite complex, requiring a nuanced understanding."

2. "El problema en cuestión es bastante complejo, requiriendo una comprensión matizada."

3. "Her feelings towards the situation are incredibly complex, mixing joy, sadness, and confusion."

4. "Sus sentimientos hacia la situación son increíblemente complejos, mezclando alegría, tristeza y confusión."

5. "The project has many complex layers that need to be addressed carefully."

6. "El proyecto tiene muchas capas complejas que deben ser tratadas con cuidado."

7. "Navigating the world of finance can be complex and overwhelming for many."

8. "Navegar por el mundo de las finanzas puede ser complejo y abrumador para muchos."

Etymology

The term "complex" comes from the Latin word complexus, meaning "composed of," from complecti, which means "to weave together." The term "number" originates from the Latin numerus. The combination thus implies a type of number that constitutes a weave of both real and imaginary components.

Synonyms and Antonyms

Synonyms: - Imaginary number (when referring to the imaginary part) - Real number (in some contexts, if talking about just the real component)

Antonyms: - Real number (in context where they are distinguished) - Rational number (if focusing specifically on rational components)

Note: The concept of complex numbers transcends basic synonyms and antonyms due to the specialized nature of the term.