Question

What is the multiplicative identity of the complex number -3+5i?
I'm having a hard time understanding multiplicative identities and this question is on my assignment. Please help!

Answer 1

the multiplicative identity it 1
since for any a in the complex number we have a*1=1*a=a

Answer 2

If however you mean multiplicative inverse of a
then you need a number such that when you multiply it to a you get 1.

Answer 3

for example the multiplicative inverse of 2 is 1/2
because 2*(1/2)=1

Answer 4

your wrong

Answer 5

if you wanted the multiplicative inverse of -3+5i
then you would need to figure out for what complex number z
you have (-3+5i)z=1

Answer 6

No

Answer 7

The answer is abviously simple if u just do all the math and put all the clues together the pie represents about a week ago. see(-3+5i)z= 3.249

Answer 8

anyways z is a complex number
z=a+bi
just multiply (-3+5i) and (a+bi) as a first step
if indeed it is the multiplicative inverse you seek

Answer 9

then you will compare both sides to find out what a and b should be

Answer 10

nononononononononononnonononononononoononononononoonoooooo

Answer 11

for example say we wanted to find the multiplicative inverse of 2-5i
then say it is a+bi
so we have that (2-5i)(a+bi)=1
multiply the left hand side \[2a+2bi-5ia-5bi^2=1 \\ 2a+2bi-5ai-5b(-1)=1 \\ 2a+(2b-5a)i+5b=1 \\ (2a+5b)+(2b-5a)i=1 \\ \text{ you have two equations to solve } \\ 2a+5b=1 \text{ and } 2b-5a=0 \]

Answer 12

so you have 2a+5b=1
and 2b=5a => b=5a/2
plug that into 2a+5b=1
so you have 2a+5(5a/2)=1
therefore 2a+25a/2=2
=> 4a+25a=2
a=2/29
so b=5a/2=5/2* 2/29=5/29

Answer 13

so the multiplicative inverse of (2-5i) is (2/29+5i/29)

Answer 14

Thank you both! You have given me much to think about.