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Complex Numbers

Complex Numbers. 1. Simplifying. 2. Addition & Subtraction. 3. Multiplication. Remember: Imaginary Number ( i ). Defined as: Powers of i. Simplifying Monomials. Simplify a Power of i Steps Separate i into a power of 2 or 4 taken to another power

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Complex Numbers

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  1. Complex Numbers 1 Simplifying 2 Addition & Subtraction 3 Multiplication

  2. Remember: Imaginary Number (i) • Defined as: • Powers of i

  3. Simplifying Monomials • Simplify a Power of i • Steps • Separate i into a power of 2 or 4 taken to another power • Use power of i rules to simplify i into -1 or 1 • Take -1 or 1 to the power indicated • Recombine any leftover parts

  4. Operations • Simplify a Power of i Simplify

  5. Simplifying Monomials Example • Square Roots of Negative Numbers Simplify

  6. Addition & Subtraction • Add and Subtract Complex Numbers • Treat i like a variable Simplify

  7. Addition & Subtraction Examples Ex: Ex: Ex:

  8. Multiplying Complex Numbers • Multiply Pure Imaginary Numbers • Steps • Multiply real parts • Multiply imaginary parts • Use rules of i to simplify imaginary parts

  9. Monomial Multiplication Example • Multiply Pure Imaginary Numbers Simplify

  10. Multiplication Example • Multiply Complex Numbers Simplify

  11. Solving ax2+b=0 • Equation With Imaginary Solutions Solve Note: ± is placed in the answer because both 4 and -4 squared equal 16

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