Addition and Subtraction of complex numbers When adding, or subtracting two (or more) complex numbers, we add/subtract the real parts and separately add /subtract the imaginary parts. The following examples illustrate this: Example 1: (3 + 7i) + (4 6i) = 3 + 7i + 4 6i……….[Remove brackets] – – = (3 + 4) + (7i 6i) like terms] – ……..[Collect = 7 + i…………………[Simplify]… Example 2: (4 + (2 5i) = 4 + 7i 2 + 5i……….[Remove brackets] 7i) – – – = (4 2) + (7i + 5i)…….[Collect like terms] – = 2 + 12i …………….[Simplify] Example 3: From 7 + 2i subtract 8 4i – Solution: Identify the and the subtrahend minuend Then proceed as follows: 7 + 2i (8 4i) = 7 + 2i 8 + 4i……………….[Remove brackets] – – – = 7 8 + (2i + 4i)……………[Collect like terms] – = 1 + 6i – ……………………[Simplify] Activity 4: Simplify each of the following expressions a) (8 + 4i) + (2 6i) b) (– 7 + 3i) +(8 – –4i) c) 2–4i + 3(–1 + 2i) d) 4(–2 + 5i) + 5(7i + 2) e) 8 +3i 7 2i f) (7 + 6i) (4 2i) – – – – g) 2(9 3i) 4(2 6i) h) 24 + 3i + 2(5i 3) – – – – Determine the values of and in each of the following equations. x y + = 4 2i x yi – + + 3 2i = 4(–2 + 5i) x yi – 2x + 3yi = 6i x – – (x + + ( = 7 + 2i y) x y)i –
Addition and Subtraction of complex numbers When adding, or subtracting two (or more) complex numbers, we add/subtract the real parts and separately add /subtract the imaginary parts. The following examples illustrate this: Example 1: (3 + 7i) + (4 – 6i) = 3 + 7i + 4 – 6i……….[Remove brackets] = (3 + 4) + (7i – 6i) ……..[Collect like terms] = 7 + i…………………[Simplify]… Example 2: (4 + 7i) – (2 – 5i) = 4 + 7i – 2 + 5i……….[Remove brackets] = (4 – 2) + (7i + 5i)…….[Collect like terms] = 2 + 12i …………….[Simplify] Example 3: From 7 + 2i subtract 8 – 4i Solution: Identify the subtrahend and the minuend Then proceed as follows: 7 + 2i – (8 – 4i) = 7 + 2i – 8 + 4i……………….[Remove brackets] = 7 – 8 + (2i + 4i)……………[Collect like terms] = – 1 + 6i ……………………[Simplify] Activity 4: Simplify each of the following expressions a) (8 + 4i) + (2 – 6i) b) (– 7 + 3i) +(8 –4i) c) 2–4i + 3(–1 + 2i) d) 4(–2 + 5i) + 5(7i + 2) e) 8 +3i – 7 – 2i f) (7 + 6i) – (4 – 2i) g) 2(9 – 3i) – 4(2 – 6i) h) 24 + 3i + 2(5i – 3) Determine the values of x and y in each of the following equations. x + yi = 4 – 2i x + yi + 3 – 2i = 4(–2 + 5i) 2x + 3yi = – x – 6i (x + y) + ( x – y)i = 7 + 2i