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Complex Numbers

Dive into the world of complex numbers, where real and imaginary parts combine in the form a+bi. Discover how to solve, add, subtract, multiply, and divide complex numbers. Learn about imaginary unit i and complex conjugates.

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Complex Numbers

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  1. Complex Numbers

  2. Solve

  3. Let me introduce you to our imaginary number i

  4. Just by knowing the first 4 you can evaluate i to any power  Think about it….

  5. Complex Numbers have both real and imaginary parts; in the form a+bi (standard form) If b≠0, a+bi is an imaginary number If b=0, a+bi is a real number If a=0, a+bi is a pure imaginary number

  6. Two complex numbers a+bi and c+di, written in standard form, are equal to each other a+bi=c+di if and only if a=c and b=d

  7. Operations with Complex Numbers Addition and Subtraction of Complex Numbers • Sum: (a+bi) + (c+di)=(a+c) + (b+d)i • Difference: (a+bi) - (c+di)=(a-c) + (b-d)i

  8. Let’s Try Some (3-i) + (2+3i) 2i + (-4 - 2i)  3 – (-2+3i) + (-5 +i) (3+2i) + (4 - i) – (7+i)

  9. Multiplying Complex Numbers 4(-2+3i) (i)(-3i)  (2-i)(4+3i) (3+2i)(3-2i) (3+2i)2

  10. Complex Conjugates and Division a+bi and a-bi are complex conjugates; their product is a real number Multiply numerator and denominator by the complex conjugate

  11. Principal Square Root of a Negative Number:

  12. Solve for x.

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