Question

Choose the multiplicative inverse.

4 + 3i

Answer 1

the snappy answer is
\[\frac{1}{4+3i}\] but that is not in standard form.

Answer 2

standard form is
\[\frac{4}{25}-\frac{3}{25}i\]

Answer 3

4-3i/25

Answer 4

if you need steps let me know

Answer 5

I'd like to know the steps.. I've never heard the term multipicative inverse before.

Answer 6

well i did not asked the question too, but i'd like to see too :D

Answer 7

multiplicative inverse of a complex number is that number which on multiplication with the original number would give you 1
for a complex number z multiplicative inverse is

Answer 8

ok the trick is (unless you just want a formula) to multiply
\[\frac{1}{4+3i}\times \frac{4-3i}{4-3i}\] the denominator is easy because
\[(a+bi)(a-bi)=a^2+b^2\] and the numerator is easy also because
\[1(a-bi)=a-bi\] so you get
\[\frac{a-bi}{a^2+b^2}\] or
\[\frac{a}{a^2+b^2}-\frac{b}{a^2+b^2}i\] in standard form

Answer 9

so for example the multiplicative inverse of
\[4+3i\] is
\[\frac{4}{25}-\frac{3}{25}i\] and the multiplicative inverse of
\[2-5i\] is
\[\frac{2}{29}+\frac{5}{29}i\]

Answer 10

thanks for remark :D