Question

Evaluate the expression 4-7i/7+4i

Answer 1

The answer is negative i because they cancel each other out except for the i

Answer 2

Multiply by (7−4i)/(7−4i) to make the denominator of (4−7i)/(7+4i) real.
(4−7i/7+4i)(7−4i/7−4i)

Expand (7+4i)(7−4i) using the FOIL Method.
(4−7i)(7−4i)/7(7)+7(−4i)+4i(7)+4i(−4i)

Simplify.
(4−7i)(7−4i)/65

Expand (4−7i)(7−4i) using the FOIL Method.
4(7)+4(−4i)−7i(7)−7i(−4i)/65

Simplify each term.
28−16i−49i−28/65

Simplify
−65i/65

−i