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GUIDED NOTES – Lesson 2-5 Complex Numbers Name: ______________________ Period: ___ Objective: I can add, subtract, multiply, and divide with complex numbers. Sometimes we will encounter equations that have no real solutions, so we have to rely on a number system with the imaginary unit, indicated by the letter _____. We can take the square root of positive numbers like answer is _______. 9 equals _____ because _____ = 9, technically the correct But when we try to take the square root of a negative number like 9 we can’t do it because no number multiplied by itself will give you a negative. It has to be either (3)(3) = 9 or (-3)(-3) = 9. IMAGINARY NUMBERS i 1 i 1 2 EXAMPLES: 121 28 (5)( 2i ) (3i )( 2i ) A COMPLEX NUMBER is a combination of a _____________ number and an ________________ number. You can add and subtract complex numbers in the same way you have combined algebraic expressions. Keep your real terms and imaginary parts _____________________. (-2 + 5i) + (1 – 7i) (4 + 6i) – (-1 + 2i) When you multiply complex numbers use the ______________ method that you are already familiar with. Then combine like parts. However you must simplify further by replacing i2 with _____. (2 + 4i)(9 – 3i) (1 + 4i)(3 – 6i) COMPLEX CONJUGATES - When dividing complex numbers, your final answer can’t have ____ in the denominator. 2+3𝑖 8 2+𝑖 𝑖 1+2𝑖 1−𝑖 SOLVING QUADRATIC EQUATIONS 5x2 + 20 = 0 3x2 + 5 = -67