What is the additive inverse of the complex number -12 + 4i?

Solution:

Given complex number -12 + 4i

The additive inverse of a number is an identity which when added to the original number results in a zero.

-5 is an additive identity of 5 and thus

-5 + 5 = 0

Similarly -5 is the additive inverse of 5, thus

= 5 + (-5)

= 5 - 5

= 0

A similar analogy is adopted for complex numbers. The given complex number is Z = -12 + 4i.

The additive inverse of the complex number will be: -Z = -(-12 + 4i)

=12-4i

Let us verify the answer.

-12 + 4i + (12 - 4i)

= -12 + 12 + 4i - 4i

= 0 + 0i

= 0

The additive inverse of the complex number is 12-4i.

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What is the additive inverse of the complex number -12 + 4i?

Summary:

The additive inverse of the complex number -12 + 4i is 12 - 4i.