What is the multiplicative inverse of complex number i?

Hint: The multiplicative inverse of complex number$z=\dfrac{1}{z}$. Since there are no real numbers that satisfy this condition, $i$ is termed as an imaginary number. Multiplicative inverse of complex numbers is simply the reciprocal of the number. In the question here we have $z=4-3i$.

What is the multiplicative inverse of 1 I?

Given, 1+i is a complex number. The multiplicative inverse of 1+i is 1/1+i. Therefore, the multiplicative inverse of 1+i is 1/2 (1-i).

How do you find the multiplicative inverse of I?

For the multiplicative inverse of a real number, divide 1 by the number. For example, the reciprocal of 5 is one fifth (1/5 or 0.2), and the reciprocal of 0.25 is 1 divided by 0.25, or 4.

What is the multiplicative identity of complex number?

Hence, multiplication of complex-numbers is commutative. Hence the multiplicative identity of the complex number is 1.

What is the multiplicative inverse of 3 I?

1/3
Thus the multiplicative inverse of 3 is 1/3.

What is the multiplicative inverse of 1 3?

Likewise the multiplicative inverse of 1 1/3 is 3/4.

Does 1 have a multiplicative inverse?

The multiplicative inverse of 1 is 1.

What is the multiplicative inverse of 5 11?

The multiplicative inverse = -(5/11)….

What is the multiplicative inverse of 1 2?

2
Answer: The multiplicative inverse or reciprocal of 1/2 is 2.

Are complex numbers distributive?

4. Commutative, Associative, Distributive Properties: All complex numbers are commutative and associative under addition and multiplication, and multiplication distributes over addition.

What is the additive inverse of 5 I?

The additive inverse of 5 is -5.

What is the inverse of a complex number?

The additive inverse of any number is that number when added to the original number results in , in other words . That is because for all . In order to add two complex numbers, you add the real parts and then add the real coefficients of the imaginary parts, thus:

What is an example of multiplicative inverse property?

Multiplicative inverse property. If you multiply two numbers and the product is 1, we call the two numbers multiplicative inverses or reciprocals of each other. For example, 4 is the multiplicative inverse of 1/4 because 4 × 1/4 = 1. 1/4 is also the multiplicative inverse of 4 because 1/4 × 4 = 1.

What is the inverse of multiplication?

The inverse operation of multiplication is division. For example, since 4 multiplied by 3 equals 12, then 12 divided by 3 equals 4. Multiplication by 3, followed by division by 3, yields the original number (since the division of a number other than 0 by itself equals 1).

What is an inverse property of multiplication?

The inverse property of multiplication states that a number multiplied by its reciprocal equals 1. The reciprocal of 1/2 is 2/1, or 2.