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how do you multiply conjugates

 Jul 6, 2015

Best Answer 

 #1
avatar+23245 
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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

 Jul 6, 2015
 #1
avatar+23245 
+5
Best Answer

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

geno3141 Jul 6, 2015

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