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Aim: Add & Subtract Complex Numbers Course: Adv. Alg. & Trig. Aim: How do we add and subtract complex numbers? Do Now: Simplify:

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Presentation on theme: "Aim: Add & Subtract Complex Numbers Course: Adv. Alg. & Trig. Aim: How do we add and subtract complex numbers? Do Now: Simplify:"— Presentation transcript:

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2 Aim: Add & Subtract Complex Numbers Course: Adv. Alg. & Trig. Aim: How do we add and subtract complex numbers? Do Now: Simplify:

3 Aim: Add & Subtract Complex Numbers Course: Adv. Alg. & Trig. Adding Complex Numbers (2 + 3i) + (5 + i) = (2 + 5) + (3i + i) = 7 + 4i In general, addition of complex numbers: (a + bi) + (c + di) = (a + c) + (b + d)i Find the sum of Combine the real parts and the imaginary parts separately. convert to complex numbers combine reals and imaginary parts separately

4 Aim: Add & Subtract Complex Numbers Course: Adv. Alg. & Trig. Subtracting Complex Numbers (1 + 3i) – (3 + 2i) = (1 + 3i) + (-3 – 2i) = -2 + i Subtract What is the additive inverse of 2 + 3i? -(2 + 3i) or -2 – 3i Subtraction is the addition of an additive inverse In general, subtraction of complex numbers: (a + bi) – (c + di) = (a – c) + (b – d)i change to addition problem combine reals and imaginary parts separately

5 Aim: Add & Subtract Complex Numbers Course: Adv. Alg. & Trig. x 1 23456 -5-4-3-2 0 i 2i 3i 4i 5i -4i -3i -2i -i -5i -6i yi Adding Complex Numbers Graphically (2 + 3i) (2 + 3i) + (3 + 0i) (3 + 0i) (5 + 3i) = (2 + 3) + (3i + 0i) = = 5 + 3i vector: 2 + 3i vector: 3 + 0i vector: 5 + 3i

6 Aim: Add & Subtract Complex Numbers Course: Adv. Alg. & Trig. Adding Vectors Vector - a directed line segment that represents directed force notation: OS R The vectors that represent the applied forces form two adjacent sides of a parallelogram, and the vector that represents the resultant force is the diagonal of this parallelogram. O P S resultant force

7 Aim: Add & Subtract Complex Numbers Course: Adv. Alg. & Trig. x 1 23456 -5-4-3-2 0 i 2i 3i 4i 5i -4i -3i -2i -i -5i -6i yi Subtracting Complex Numbers Graphically (1 + 3i) (1 + 3i) – (3 + 2i) (3 + 2i) = (1 + 3i) + (-3 – 2i) = -2 + i (-3 – 2i) (-2 + i) The vector representing the additive inverse is the image of the vector reflected through the origin. Or the image under a rotation about the origin of 180 0.

8 Aim: Add & Subtract Complex Numbers Course: Adv. Alg. & Trig. Model Problems Add/Subtract and simplify: (10 + 3i) + (5 + 8i) (4 – 2i) + (-3 + 2i) Express the difference of in form a + bi = 15 + 11i = 1


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