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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 NumbersAlgebra of Complex Numbers

### Equivalence of complex numbers

When two complex numbers are considered to be equal?

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When will two complex numbers z_1=a+ib and z_2=p+iq be equal?

• when modulus are equal |z_1| = |z_2|
• when argument are equal text(arg)z_1 = text(arg)z_2
• when real and imaginary parts are equal a=p and b=q
• when real and imaginary parts are equal a=p and b=q
• when real or imaginary parts are equal a=p or b=q

The answer is 'if real and imaginary parts are equal a=p and b=q'

Two complex numbers are equal if real and imaginary parts are equal.

Complex numbers Equivalence: Two complex numbers z_1=a_1+ib_1 and z_2=a_2+ib_2 are equal only if a_1=a_2 and b_1=b_2

Solved Exercise Problem:

If two complex numbers 3-i4 and 1+x are equal, What is x?

• -4
• 2-i4
• 2-i4
• 3-i4
• -4i

The answer is '2-i4'

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