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Thought-Process to Discover Knowledge

Welcome to nubtrek.

Books and other education websites provide "matter-of-fact" knowledge. Instead, nubtrek provides a thought-process to discover knowledge.

In each of the topic, the outline of the thought-process, for that topic, is provided for learners and educators.

Read in the blogs more about the unique learning experience at nubtrek.
mathsComplex NumbersProperties of Complex Number Arithmetic

### Addition : Associative Law

Complex addition is associative : Order of addition can be changed.

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What does 'Associate' mean? • to connect with; to join
• to connect with; to join
• to separate

The answer is 'to connect with; to join'

When three complex numbers are added,
•  Person A associates the middle complex number with first complex number and, to the result of that, he adds the third complex number (z_1 + z_2) + z_3
•  Person B associates the middle complex number with third complex number and to that she adds the first complex number z_1 + (z_2+z_3)

will the two persons get different results?

• They will get different results.
• They will get identical results
• They will get identical results

The answer is 'They will get identical results'.

•  Order of addition can be changed - associative.

Associative Property of Complex Addition: For Any complex number z_1,z_2,z_3 in CC,
z_1+(z_2+z_3) = (z_1+z_2)+z_3

Is Associative property applicable to subtraction?

• when subtraction is handled as inverse of addition.
• when subtraction is handled as inverse of addition.
• yes. Order of subtraction can be swapped

The answer is 'when subtraction is handled as inverse of addition'. For (z_1 - z_2) - z_3, it will be considered as (z_1 + (-z_2)) + (-z_3).

Solved Exercise Problem:

Given z_1, z_2 in CC, what will be the result of z_1 + z_2 + z_1?

• 2z_1+z_2
• 2z_1+z_2
• z_1+z_2
• z_2
• z_1+2z_2

The answer is '2z_1+z_2'.

slide-show version coming soon