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The additive inverse of a complex number a + bi is the complex number x + yi such that a + bi + x + yi = 0
Solve for x and y using a + bi + x + yi = 0
a + bi + x + yi = 0
Subtract x from each side of the equation
a + bi + x - x + yi = 0 - x
a + bi + yi = 0 - x
Subtract yi from each side of the equation
a + bi + yi - yi = 0 - x - yi
a + bi = - x - yi
Now, you can compare the real parts and the imaginary parts of a + bi = - x - yi
We get a = -x and b = -y
When a = -x, x = -a
When b = -y, y = -b
The additive inverse is x + yi = -a + -bi
Example #1:
Find the additive inverse of 4 + -5i
The additive inverse of 4 + 5i is the complex number x + yi such that
4 + -5i + x + yi = 0
4 + -5i = - x - yi
Compare the real parts and the imaginary parts of 4 + -5i = - x - yi
We get -x = 4 and -y = -5
When -x = 4, x = -4
When -y = -5, y = 5
The additive inverse of 4 + -5i is the complex number -4 + 5i
Example #2:
Find the additive inverse of -2 + -6i
The additive inverse of -2 + -6i is the complex number x + yi such that
-2 + -6i + x + yi = 0
-2 + -6i = - x - yi
Compare the real parts and the imaginary parts of -2 + -6i = - x - yi
We get -x = -2 and -y = -6
When -x = -2, x = 2
When -y = -6, y = 6
The additive inverse of -2 + -6i is the complex number 2 + 6i
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