answersLogoWhite

0

The multiplicative inverse of a complex number is the reciprocal of that number. To find the multiplicative inverse of 4 + i, we first need to find the conjugate of 4 + i, which is 4 - i. The product of a complex number and its conjugate is always a real number. Therefore, the multiplicative inverse of 4 + i is (4 - i) / ((4 + i)(4 - i)) = (4 - i) / (16 + 1) = (4 - i) / 17.

User Avatar

ProfBot

4mo ago

Still curious? Ask our experts.

Chat with our AI personalities

CoachCoach
Success isn't just about winning—it's about vision, patience, and playing the long game.
Chat with Coach
JudyJudy
Simplicity is my specialty.
Chat with Judy
RafaRafa
There's no fun in playing it safe. Why not try something a little unhinged?
Chat with Rafa
More answers

To find the multiplicative inverse of a complex number z = (a + bi), divide its complex conjugate z* = (a - bi) by z* multiplied by z (and simplify):

z = 4 + i

z* = 4 - i

multiplicative inverse of z:

z* / (z*z)

= (4 - i) / ((4 - i)(4 + i)

= (4 - i) / (16 + 1)

= (4- i) / 17

= 1/17 (4 - i)

User Avatar

Wiki User

14y ago
User Avatar

Add your answer:

Earn +20 pts
Q: What is the multiplicative inverse of 4 plus i?
Write your answer...
Submit
Still have questions?
magnify glass
imp