What is the conjugate of # 7 - 4i#?

1 Answer
Dec 3, 2015

Answer:

#7+4i#

Explanation:

The complex conjugate of #a+bi# is #a-bi#. Complex conjugates have the cool property that #(a+bi)(a-bi)=a^2-abi+abi-b^2i^2=a^2+b^2=|a+bi|^{2}#. This makes them useful for rewriting quotients #(a+bi)/(c+di)# in the standard form #alpha+beta i#.

For example,

#(3+2i)/(7-4i)=(3+2i)/(7-4i) * (7+4i)/(7+4i)=(21+12i+14i+8i^2)/(49-16i^2)#

#=(13+26i)/(49+16)=13/65+26/65 i=1/5 + 2/5 i#