Complex numbers Algebra II Dr. Guram.

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Presentation transcript:

Complex numbers Algebra II Dr. Guram

How do we perform operations with complex numbers?. Focus Questions How do we perform operations with complex numbers?. What is an example of a real- world scenario utilizing complex numbers?

Curriculum standards CLE 3103.2.2, 3103.2.1, 3103.2.4, 3103.2.5, 3103.2.6, 3103.2.3 - compute with … complex numbers. Sources: http://www.corestandards.org/Math/Content/HSA/CED /A/1/ Spring Board Algebra 2 workbook Larson algebra 2 textbook

Real World Examples Utilizing complex numbers What are examples of ways we utilize factoring in real world situations? ???

Real World Examples Utilizing complex numbers Fractals: never-ending pattern. Fractals are infinitely complex patterns that are self-similar across different scales. They are created by repeating a simple process over and over in an ongoing feedback loop. They are in nature.

Academic language Imaginary unit i: 𝑖= −1 so 𝑖 2 =−1. Complex number: a number 𝑎+𝑏𝑖 where 𝑎 and 𝑏 are real numbers and 𝑖 is the imaginary unit. Imaginary number: a complex number 𝑎+𝑏𝑖 where 𝑏≠0.

Academic language Complex conjugates: two complex numbers of the form 𝑎+𝑏𝑖 and 𝑎−𝑏𝑖. Complex plane: a coordinate plane in which each point (a, b) represents a complex number 𝑎+𝑏𝑖. The horizontal axis is the real axis and the vertical axis is the imaginary axis. Absolute value of a complex number: if z =𝑎+𝑏𝑖 then the absolute value of z, denoted 𝑧 = √( 𝑎 2 + 𝑏 2 ) .

Square root of a negative number

Solving a Quadratic equation with complex numbers

practice examples

Complex numbers

Complex numbers

Practice problems

Example #4

Example #5

Example #6

Absolute value of a complex number

Example #7

How do we perform operations with complex numbers?. Review How do we perform operations with complex numbers?. What is an example of a real-world scenario utilizing complex numbers?

define the mathematical terms: complex number, and imaginary number. Review of terms define the mathematical terms: complex number, and imaginary number. Define the mathematical terms: complex conjugate, complex plane, and absolute value of a complex number.

Classwork/Homework - worksheet