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

1 Answer
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]