SAT Subject Test in Math II

The SAT Subject Test in Math II assesses students' understanding of advanced mathematical concepts and their ability to apply these concepts to solve problems.

Algebraic ManipulationFunctions and GraphsCoordinate Geometry
Complex NumbersTrigonometryLogarithmic and Exponential Functions
Modeling Real-World DataOptimization in Everyday LifeMath in Technology and Engineering
Time Management and PrioritizationSmart Use of the Calculator
Algebraic Manipulati...Functions and GraphsCoordinate GeometryComplex NumbersTrigonometryLogarithmic and Expo...Modeling Real-World ...Optimization in Ever...Math in Technology a...Time Management and ...Smart Use of the Cal...
Advanced Topics

Complex Numbers

Expanding Beyond Real Numbers

Complex numbers include both a real and an imaginary part, written as \( a + bi \), where \( i = \sqrt{-1} \).

Key Concepts

  • Addition, subtraction, multiplication, and division of complex numbers.
  • Plotting complex numbers on the complex plane.
  • Conjugates and absolute value.

Why Learn This?

Some equations, like \( x^2 + 1 = 0 \), have no real solutions. Complex numbers allow us to solve these equations, which are crucial in engineering and physics.

Tips

  • Use \( i^2 = -1 \) to simplify expressions.
  • To multiply, use distributive property and combine like terms.

Real-World Insight

Complex numbers are used in electrical engineering to analyze circuits.

Key Formula

\[z = a + bi\]

Examples

  • Simplifying \( (2 + 3i) + (4 - i) \) gives \( 6 + 2i \).

  • The absolute value of \( 3 + 4i \) is \( 5 \).

In a Nutshell

Solve and analyze equations involving imaginary and complex numbers.

Key Terms

Imaginary Unit
The symbol \( i \), which satisfies \( i^2 = -1 \).
Conjugate
For \( a + bi \), the conjugate is \( a - bi \).
Next
Trigonometry