Server Error

Server Not Reachable.

This may be due to your internet connection or the nubtrek server is offline.

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

### Conjugate of a complex Number

Conjugate of a complex number is explained.

click on the content to continue..

In numerical expressions or algebraic expressions, we can manipulate the expressions without modifying the value of the expression
•  add and subtract : eg 3 = 3+1-1
•  multiply and divide : eg : 3 = 3 xx 2/2
•  etc.

. These manipulations help to arrive at a different form of expressions or help to solve.

In case of complex numbers, a+ib, one modification stands out "convert the complex number to real number". This can be achieved either by addition or multiplication with the number a-ib.
•  addition (a+ib) + (a-ib) = 2a
•  multiplication (a+ib) xx (a-ib) = a^2+b^2

For a given complex number z= a+i b, the connected number that give a real number on multiplication is a-ib. It is named as conjugate of z and represented as bar(z) or bar(a+ib) = a-ib

What does 'conjugate' mean?

• coupled; joined ; related in reciprocal or complementary
• coupled; joined ; related in reciprocal or complementary
• disjoint; additional; unrelated and orthogonal

The answer is 'coupled; joined ; related in reciprocal or complementary'

Conjugate of a complex number is the number with the same real part and negative of imaginary part.

Conjugate of a Complex NumberFor a complex number z=a+ib in CC  the conjugate of z is given as bar(z) = a-ib.

bar(z) is called ... of z.

• Pronunciation : Say the answer once

Solved Exercise Problem:

Find bar(1-3i).

• 1-3i
• -1-3i
• 1+3i
• 1+3i
• -1+3i

The answer is '1+3i'

slide-show version coming soon