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1.5 Complex numbers

1.5 Complex numbers. Imaginary unit i -. ; used to write the square root of a negative number. Complex number – a number a + bi, where a is the real part and bi is the imaginary part. Standard form – a +bi. Imaginary number – contains i.

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1.5 Complex numbers

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  1. 1.5 Complex numbers Imaginary unit i - ; used to write the square root of a negative number Complex number – a number a + bi, where a is the real part and bi is the imaginary part Standard form – a +bi Imaginary number – contains i

  2. Complex conjugates – 2 complex numbers of the form a + bi and a – bi ; product is a real #EX: 7-2i, 7+2i Find real numbers a and b such that the equation is true: Ex1: a+bi = 13 + 4i Ex2: (a+4) +2bi = 6 – 5i

  3. i = Patterns of i

  4. So what is the pattern? Try these:

  5. Simplify l

  6. Examples: • Subtract: • Multiply: -6i(5 – 3i) • Multiply (2- i)(4 + 7i)

  7. Examples • Put in standard form: • Perform the operation:

  8. Complex plane - a coordinate plane where each point (a, b) represents a complex number a + bi. It has a horizontal real axis and a vertical imaginary axis.

  9. Plot these numbers • 2 – 3i • -5 + i • -1 – 4i • -i • 3

  10. Use the Quadratic Formula Solve

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