Welcome to the Wonderland of Complex Numbers!
Complex Number Questions
What is a complex number?
What are Real Numbers?
What are Real Numbers?
Any number which is present in a number system such as positive, negative, zero, integer, rational, irrational, fractions, etc. are real numbers. It is represented as Re(). For example: 12, -45, 0, 1/7, 2.8, √5, etc., are all real numbers.
Why are complex numbers important?
Conjugate of a Complex Number
The conjugate of the complex number is formed by taking the same real part of the complex number and changing the imaginary part of the complex number to its additive inverse. If the sum and product of two complex numbers are real numbers, then they are called conjugate complex numbers. For a complex number z = a + ib, its conjugate is z = a - ib.
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What are Imaginary Numbers?
The numbers which are not real are imaginary numbers. When we square an imaginary number, it gives a negative result. It is represented as Im(). Example: √-2, √-7, √-11 are all imaginary numbers.
Connection with the UAE
Telecommunications: The UAE has advanced telecommunications infrastructure that utilizes complex numbers for signal transmission. Architecture: Complex numbers are used in designing modern buildings and structures, facilitating calculations for stability and aesthetics. Renewable Energy: In solar energy systems, complex numbers help model and optimize performance.
Notation
Notation
An equation of the form z= a+ib, where a and b are real numbers, is defined to be a complex number. The real part is denoted by Re z = a and the imaginary part is denoted by Im z = ib.
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