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Aim: How do we add and subtract complex numbers?

Aim: How do we add and subtract complex numbers?. Do Now:. Simplify:. Find the sum of. Adding Complex Numbers. = 7 + 4 i. = (2 + 5) + (3 i + i ). (2 + 3 i ) + (5 + i ). In general, addition of complex numbers: (a + b i ) + (c + d i ) = (a + c) + (b + d) i.

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Aim: How do we add and subtract complex numbers?

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  1. Aim: How do we add and subtract complex numbers? Do Now: Simplify:

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

  3. Subtract Subtracting Complex Numbers What is the additive inverse of 2 + 3i? -(2 + 3i) or -2 – 3i Subtraction is the addition of an additive inverse = -2 + i = (1 + 3i) + (-3 – 2i) (1 + 3i) – (3 + 2i) 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

  4. yi 5i 4i vector: 2 + 3i 3i (2 + 3i) 2i (5 + 3i) (3 + 0i) vector: 3 + 0i i x 1 -5 -4 -3 -2 -1 0 2 3 4 5 6 -i -2i -3i -4i -5i -6i Adding Complex Numbers Graphically (2 + 3i) + (3 + 0i) = (2 + 3) + (3i + 0i) = = 5 + 3i vector: 5 + 3i

  5. S P resultant force OS O R Adding Vectors Vector - a directed line segment that represents directed force notation: 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.

  6. yi 5i 4i 3i (1 + 3i) 2i (3 + 2i) i (-3 – 2i) (-2 + i) x 1 -5 -4 -3 -2 -1 0 2 3 4 5 6 -i -2i -3i -4i -5i -6i Subtracting Complex Numbers Graphically (1 + 3i) – (3 + 2i) = (1 + 3i) + (-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 1800.

  7. Model Problems Add/Subtract and simplify: (10 + 3i) + (5 + 8i) = 15 + 11i (4 – 2i) + (-3 + 2i) = 1 Express the difference of in form a + bi

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