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Thought-Process to Discover Knowledge

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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.

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mathsComplex NumbersProperties of Complex Number Arithmetic

### Addition : Closure Law

Complex addition is closed: Sum or difference of two complex numbers is another complex number.

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What does 'closure' mean? • closed
• not open
• both the above
• both the above

Answer is 'both the above'

What is the "span" mean?

• Full extent of something; all that is included in that;
• Full extent of something; all that is included in that;
• past tense of spin

The answer is 'Full extent of something'

What is the span of complex numbers?

• a+ib with a,b in RR
• real and imaginary parts taking any real number
• both the above
• both the above

The answer is 'Both the above'

The span of complex numbers or the set of complex numbers is represented as CC.

When any two complex numbers are added will it result in a number within the span of complex numbers?

• Yes. It will be another complex number.
• Yes. It will be another complex number.
• No. It extends the complex numbers to something beyond the set of complex numbers.

The answer is 'Yes. It will be another complex number'

•  Sum or difference of two complex numbers is another complex number - closure property

Closure Property of Addition and Subtraction: For any given complex numbers z_1, z_2 in CC,  z_1 +- z_2 in CC.

Solved Exercise Problem:

Given a complex number z and a. What will be the sum z+a?

• a real number
• a complex number
• a complex number
• addition between a complex number and real number is not defined

The answer is 'a complex number'

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