Square Root of Complex Number

A square root of an x is a numeral r such to r2 = x, or a numeral r whose square is x. each non-negative real number x have a exclusive non-negative square root, recognized the principal square root, signify by a essential symbol as . For optimistic x, the main square root knows how to as well be written in exponent information, as x1/2.  (Source: Wikipedia)

Square Root of Complex Number:

A complex number is a number regarding of a real also imaginary part. It know how to be written in the structure a + bi, where a and b are real numbers, also i is the ordinary imaginary unit among the property i 2 = −1. The complex numbers include the ordinary factual numbers, however expand them by adding in extra numbers and equally increasing the considerate of addition also multiplication.

Every positive numbers x contain two square roots. One of them is` sqrt(x)` , to be constructive, with the other `-sqrt(x)` that is negative. Collectively, these two roots are signifying `+-sqrt(x)` . Square roots of unconstructive numbers know how to be converse in the structure of complex numbers. More commonly, square roots know how to be thinks in any context in that a notion of square of several arithmetical objects is definite.

Example for Square Root of Complex Number:

Example 1:

Solve square root of compel numbers `sqrt(3) - isqrt(6)`

Solution:

Step 1: the given square root complex number is `sqrt(3) - isqrt(6)`

Step 2: `x = sqrt(3) and y = -sqrt(6)`



Step 3:    `r =sqrt( x^2+y^2)`

Step 4: substitute x and y values

`r =sqrt( (sqrt(3)^2)+(-sqrt(6)^2))`

Step 5:   r = 3

Example 2:

Solve square root of comple numbers 4+13i

Solution:

Step 1: the given square root complex number is   4+13i

Step 2: the given problem of the form is a+bi

Step 3: `x = 4 and y = 13`

Step 4:    `r =sqrt( x^2+y^2)`

Step 5: substitute x and y values

`r =sqrt( (4^2)+(13^2))`

Step 6:    `sqrt(377)`

Step 7:   r = 19

Step 8: finding b value

` b =sqrt((r-x)/2)) `

Step 9:    ` b =sqrt(((19)-4)/2) `

Step 10:    ` b =sqrt((15)/2) `

Step 11:  b = 2

substitute y and b in a

Step 12:  a = `y/(2b)`

a = `13/(2(2))`

a = 3

Step 13: find square root of  r1 and r2

r1 =a + bi = 3 + 2i

r2 = -a-bi = -3-2i

so the square root of complex numbers are 3+2i and -3-2i