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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

### Multiplicative Identity

Complex multiplication has a multiplicative identity 1.

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What does "identical" mean?

• exactly alike; same in every detail
• exactly alike; same in every detail
• different; mismatched

The answer is "exactly alike; same in every detail"

Consider the complex number 1+i0. What will be the result of multiplying that with a complex number z_1?

• 1+i0
• z_1
• z_1

The answer is 'z_1'. The product is identical to the number being multiplied.

What is a multiplicative identity?

• an element, when multiplied, will result in product identical to the multiplicand.
• an element, when multiplied, will result in product identical to the multiplicand.
• the phrase "multiplicative identity" does not have any meaning.

The answer is 'an element, when multiplied, will result in product identical to the multiplicand'.

•  1=1+i0 is the multiplicative identity.

Multiplicative Identity in Complex Numbers: For any complex number z_1 in CC, there exists 1 = 1+i0, in CC such that
z_1 xx 1 = z_1

Solved Exercise Problem:

Consider z_1=sqrt(2)+sqrt(3)i What will be the product z_1 xx (1+i0)?

• z_1
• z_1
• 0
• 1
• i

The answer is 'z_1'

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