Algebra 2: Complex Numbers Flashcards

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Questions and Answers

What is the imaginary unit?

  • A type of real number
  • The unit in the imaginary number system (correct)
  • Represented by the symbol i (correct)
  • The square root of a negative number

What is an imaginary number?

The square root of a negative number, written in the form bi.

What is a complex number?

Any number that can be written as a + bi.

What is the real part of a complex number?

<p>a in the form a + bi.</p> Signup and view all the answers

What is the imaginary part of a complex number?

<p>b in the form a + bi.</p> Signup and view all the answers

What is the complex plane?

<p>A set of coordinate axes where the horizontal axis is the real axis and the vertical axis is the imaginary axis.</p> Signup and view all the answers

What is a complex conjugate?

<p>For a complex number a + bi, it is a - bi.</p> Signup and view all the answers

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Study Notes

Imaginary Unit

  • Denoted as i, it represents the square root of -1.
  • Fundamental in the imaginary number system.

Imaginary Number

  • Defined as the square root of a negative number.
  • Expressed in the form bi, where b is a real number.
  • Often referred to as a "pure" imaginary number.

Complex Number

  • Any number that can be expressed as a + bi, with a and b being real numbers.
  • Incorporates both a real part and an imaginary part.

Real Part of a Complex Number

  • In a complex number expressed as a + bi, the real part is a.
  • This part is plotted on the horizontal axis of the complex plane.

Imaginary Part of a Complex Number

  • In a complex number expressed as a + bi, the imaginary part is b.
  • This part is plotted on the vertical axis of the complex plane.

Complex Plane

  • A two-dimensional plane used for graphing complex numbers.
  • Consists of a horizontal axis (real axis) and a vertical axis (imaginary axis).

Complex Conjugate

  • The complex conjugate of a number a + bi is defined as a - bi.
  • Useful in various mathematical operations, such as simplifying expressions and finding magnitudes.

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