## Complex Number Shortcut Tricks

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# Introduction

In this article, we will discuss about Complex Number Shortcut Tricks , the whole chapter contains each and every concept by shortcut tricks.

Today we are to discuss the complex number, a conjugate of a complex number, modulus of a complex number, argument, or amplitude of a complex number.

Along with the above concepts, we will also discuss about trigonometric or polar form, logarithm form, eulerian form, and the square root of a complex number.

Now we are going to discuss each concept one by one by discussing their basic concepts along with shortcut tricks.

Click on the link below to buy the eBook Complex Number Shortcut Tricks

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## Complex Number

A number of the form z = x + y where x, y Є R, and = under root -1, is called a complex number where x is known as the real part, and y is known as the imaginary part of the complex number.

Note:-

1. x = Re(z) and y = Im(z)
2. if x = 0 then the complex number is known as purely imaginary and if y = 0 then the complex number is purely Real.
3. The complex number 0 is purely Real and purely imaginary both.

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## Conjugate of a Complex Number

If z = x + y is a  complex Number then its conjugate is defined as

x – y which is obtained by change the sign of imaginary part.

## Modulus of a Complex Number

If z = x + y is a complex Number then its modulus is denoted by I z I and it is defined as the square root of the sum of x square and y square.

To know more about conjugate and modulus of a complex number with their properties click on the link below to buy

To know more about complex number click on the link below to buy eBook Complex Number Shortcut Tricks

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## Amplitude  or  Argument of a Complex Number

The amplitude or argument of a complex z is the inclination of the directed line segment representing z, with the real axis.

Note:-

1. The principle value of any complex number lies between  –π < ϴ ≤ π
2. In general, by the arg z, we mean the principle arg z  unless specified otherwise.

## Polar form / Trigonometric form

If z = x + y is a complex Number in Cartesian form then its polar form is given by

Z = r (cos ϴ + i sin ϴ) where r  and arg z = ϴ

#### Eulerian Form, Logarithm of a Complex Number and Cube Root of unity are completely defined in ebook complex number shortcut tricks

To know more about complex number click on the link below to buy eBook Complex Number Shortcut Tricks

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## Shortcut Tricks

we have the following shortcut tricks to find the solution of complex numbers in just in a few seconds.

# shortcut tricks to find the locus of a point formed by the complex number.

# shortcut tricks to find the maximum and minimum value of the modulus of a complex number.

# shortcut tricks to find the square root of a complex number.

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## Explanations

Each mcq is explained by proper shortcut tricks in a simple manner.

To find the correct explanation of each and every MCQ and the complete test series click on the link below

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## Conclusion

Finally, we can say that complex number shortcut tricks help us to solve the questions of complex numbers very easily and in less time.

If you are intersted to buy the ebook of Complex Number Shortcut Tricks

then click on the link below

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Nitin Sharma

### Nitin Sharma

Hello Dosto ....This is Nitin Sharma working as a Mathematician, Writer, You Tuber, Blogger, Lyricist, and Author. By this platform, I express my knowledge and my passion by writing Articles on Mathematical Concepts. I hope you are enjoying it. Thank You!