GRE Subject Test: Math

The GRE Subject Test in Math assesses knowledge and skills in undergraduate-level mathematics, including calculus, algebra, and geometry.

Algebra FundamentalsCalculus ConceptsGeometry Essentials
Abstract AlgebraReal AnalysisComplex Numbers and Functions
Mathematics in EngineeringFinance and EconomicsTechnology and Computer Science
Time Management for GRE MathProcess of Elimination
Algebra FundamentalsCalculus ConceptsGeometry EssentialsAbstract AlgebraReal AnalysisComplex Numbers and ...Mathematics in Engin...Finance and Economic...Technology and Compu...Time Management for ...Process of Eliminati...
Advanced Topics

Complex Numbers and Functions

Exploring the Imaginary and Beyond

Complex numbers extend the real numbers by introducing \(i\), where \(i^2 = -1\). This opens up a fascinating world of new mathematical possibilities.

Working with Complex Numbers

  • Form: \(a + bi\), where \(a\) and \(b\) are real numbers.
  • Addition & Multiplication: Follow the same rules as real numbers, but remember \(i^2 = -1\).
  • Complex Functions: Functions can take complex inputs and produce complex outputs.

Why Learn This?

Complex numbers are used in engineering, physics, and even in visual effects in movies.

Practice

  • Add \(2 + 3i\) and \(1 - 4i\).
  • Multiply \(3i\) by \(2 - i\).

Examples

  • \(2 + 3i\) plus \(1 - 4i\) is \(3 - i\).

  • \(3i\) times \(2 - i\) is \(6i - 3i^2 = 6i + 3\).

In a Nutshell

Complex numbers combine real and imaginary parts and are vital in advanced mathematics and engineering.

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Mathematics in Engineering