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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.

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## Complex Number

A number of the form z = x + *ἱ *y where x, y Є **R, **and *ἱ *= 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:-**

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

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**Conjugate of a Complex Number**

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

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

**Modulus of a Complex Number**

If z = x + *ἱ *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:-**

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

**Polar form / Trigonometric form**

If z = x + *ἱ *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.

To know about the shortcut tricks click on the link below

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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.

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then click on the link below

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