write 1/(1+2i) in the form of a+bi.

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baxthum8 | High School Teacher | (Level 3) Associate Educator

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In order to write in form a + bi we must conjugate the denominator.  In other words multiply both the numerator and denominator by the conjugate of (1+2i) which is (1 - 2i).  It will look like this:

`1/(1+2i)* (1-2i)/(1-2i)` I can do this because this value is equivalent to 1.  Multiplying by 1 does not change value of original expression.

Multiplying numerators gives me:  `1 - 2i`

Multiplying denominators is the difference of 2 squares.  (I can use foil in which middle terms cancel each other.)

`(1+2i)(1-2i) = 1 -2i + 2i - 4i^2`

Since `i^2` equals -1 this expression simplifys to `1 - (-4) = 5`

Therefore we have  `(1-2i)/5`

Written in a+bi form this is:  `1/5 -2/5i`