How do I simplify 7/(7+5i)? (Hint: The irrational number i equals 1 when i^2.)

1 Answer
Alan N.
Dec 17, 2017

#(49-35i)/74#

Explanation:

Let #z=7/(7+5i)#

The complex conjugate of #(7+5i)# is #(7-5i)#

We can write #z= (7(7-5i))/ ((7+5i)(7-5i))#

Now remember that #(a+bi)(a-bi) = a^2 + b^2#

#:.z= (7(7-5i))/(7^2+5^2)#

#= (49-35i)/(49+25)#

#=(49-35i)/74#

[Comment: The "hint" is misleading. #i# is referred to as the imaginary unit. It is neither rational nor irrational as both are within the set of real numbers. #i^2 =-1#]

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