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Thought-Process to Discover Knowledge

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mathsComplex NumbersProperties of Complex Number Arithmetic

Complex numbers have additive inverse - negative of the number.

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What does 'inverse' mean?

• same; identical; similar
• opposite; converse
• opposite; converse

Consider two complex numbers z_1 = a+ i b and z_2 = -a-ib. What will be z_1+z_2?

• 0+0i
• 0
• All the above
• All the above

The answer is 'All the above'. -z is called the additive inverse for z as z+(-z) = 0.

•  For any complex number z there exits -z - additive inverse.

Additive Inverse: For any complex number z = a+ib in CC, there exists -z = -a - i b in CC such that
z + (-z) = 0

Solved Exercise Problem:

What is the additive inverse of 3.5+2.1i?

• -3.5+2.1i
• 3.5-2.1i
• -3.5-2.1i
• 0

The answer is '-3.5-2.1i'

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