Question 212963
Perform the indicated operation. write answer in standard form


{{{(1+8i)(6+4i)}}}


Step 1.  Using the FOIL method, we have


{{{(1+8i)(6+4i)= 1*6+8i*6+1*4i+(8i)(4i)}}}


{{{(1+8i)(6+4i)= 6+48i+4i+32i^2}}}


{{{(1+8i)(6+4i)= 6+52i-32}}}


where {{{i^2=-1}}} since {{{sqqrt(-1)*sqrt(-1)=-1}}} and {{{i=sqrt(-1)}}}.


As a result, {{{32i^2=-32}}} was used in the previous equation


Simplifying the last equation yields the following


{{{(1+8i)(6+4i)= -26+52i}}}


Step 2.  Answer is {{{(1+8i)(6+4i)= -26+52i}}}


I hope the above steps were helpful.


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Good luck in your studies!


Respectfully,
Dr J