Question

how do you find the multiplicative inverse of a complex number?

Answer 1

you want the answer or the method?

Answer 2

method

Answer 3

ok suppose you are given
\[a+bi\] and you want to solve
\[(a+bi)(x+iy)=1\] for x and y. this is the same as solving
\[x+iy=\frac{1}{a+bi}\] for x and y, and you compute
\[\frac{1}{a+bi}\] as you would any complex division

Answer 4

multiply numerator and denominator by the conjugate of the denominator
\[\frac{1}{a+bi}\times \frac{a-bi}{a-bi}\] and write your answer in standard form

Answer 5

so what if it's 4i/(3+1)

Answer 6

you lost me there.
\[\frac{4i}{3+1}=\frac{4i}{4}=i\]

Answer 7

multiplicative inverse of
\[i\] is
\[-i\] because
\[i\times -1=1\]