How do you simplify #1/(2+5i )#?

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Answer 1 · 2015-11-07T23:10:30

#(2-5i)/(29)#

Multiply by a special form of #1#. To figure out what that special form of #1# is, we take the complex conjugate of the bottom divided by itself.

That's just a fancy way of saying switch the sign in front of the imaginary term and do this:

#(2-5i)/(2-5i)#

now we multiply our original expression by that:

#1/(2+5i) * (2-5i)/(2-5i)#

#(2-5i)/((2+5i)(2-5i))#

#(2-5i)/(4-25i^2)#

#(2-5i)/(4+25)#

#(2-5i)/(29)#