An example of conjugates is: a + bi and a - bi
Multiply them as you would any two binomials, using First, Outside, Inside, Last:
(a + bi)(a - bi) = a·a + a(-bi) + (bi)a - (bi)(bi)
= a2 - abi + abi - b2i2
Since i2 = -1: = a2 - (b2)(-1)
= a2 + b2
This gives you a formula: (a + bi)(a - bi) = a2 + b2
Example: (3 + 4i)(3 - 4i) = 32 + 42 = 9 + 16 = 25
Example: (3x + 4yi)(3x - 4yi) = (3x)2 + (4y)2 = 9x2 + 16y2
An example of conjugates is: a + bi and a - bi
Multiply them as you would any two binomials, using First, Outside, Inside, Last:
(a + bi)(a - bi) = a·a + a(-bi) + (bi)a - (bi)(bi)
= a2 - abi + abi - b2i2
Since i2 = -1: = a2 - (b2)(-1)
= a2 + b2
This gives you a formula: (a + bi)(a - bi) = a2 + b2
Example: (3 + 4i)(3 - 4i) = 32 + 42 = 9 + 16 = 25
Example: (3x + 4yi)(3x - 4yi) = (3x)2 + (4y)2 = 9x2 + 16y2