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Evaluate 1 + i/2 + 1/4 + i/8 + 1/16 + i/32 + ... (where i is the imaginary unit).  Express your answer in the form a+bi, where a and b are real.

 May 29, 2021
 #1
avatar+602 
+1

Don't be scared.

It's $1+i\left(\frac{1}{2}+\frac{1}{4}+\frac{1}{8}+...\right)=1+i$.

 May 30, 2021
 #2
avatar+34340 
+1

Following thedude's work

 

=   1   + (1/4 + 1/16 .....) + i ( 1/2 + 1/8 + 1/32......)

  =  1   +  1/4 / ( 1-1/4)     + i ( 1/2 / (1-1/4) )

  =   1  + 1/3 + i 2/3

= 1 1/3   + 2/3 i

 May 30, 2021

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