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105
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Simplify this complex number.

 

 Aug 8, 2020
 #1
avatar+21958 
0

There are several ways to approach this; I'm going to rationalize the denominator of each term first.

 

[ 1 / (1 + 2i) ] · [ (1 - 2i) / (1 - 2i) ]  =  (1 - 2i) / 5

[ 3 / (1 - i) ] · [ (1 + i) / (1 + i) ]  =  3(1 + i) / 2

[ (3 -2i) / (1 + 3i) ] · [ (1 - 3i) / (1 - 3i) ]  =  (-3 - 11i) / 10

 

[ 1 / (1 + 2i) + 3 / (1 - i) ]  =  [ (1 - 2i) / 5 + 3(1 + i) / 2 ]  =  (17 + 11i) / 10

 

[ (17 + 11i) / 10 ] · [ (-3 - 11i) / 10 ]  =  (70 - 220i) / 100  =  7/10 - (11/5)i

 Aug 8, 2020

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