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.
Still curious? Ask our experts.
Chat with our AI personalities
Lao
Vivi
ReneTo 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)
Add your answer:
Earn +20 pts
What is the multiplicative inverse of -0.25?
The multiplicative inverse of a number is the reciprocal of that number. In this case, the multiplicative inverse of -0.25 is -1 / -0.25, which simplifies to -4. This is because multiplying a number by its multiplicative inverse results in a product of 1, the multiplicative identity.
What is the multiplicative inverse of -4-y?
If y is equal to -4 there is not a multiplicative inverse. If y is different than -4 the inverse is: -1/(4+y)
What is the multiplicative of -1?
Assuming the question is about the multiplicative inverse, the answer is, -1. It is its own multiplicative inverse.
What is the multiplicative inverse of negative 4 over 3?
Flip it upside down. Now you have negative three over four. That's your multiplicative inverse (reciprocal) -3/4
What is the multiplicative inverse of negative 9?
-9; the multiplicative inverse: -1/9
