Square Root 2 + 3i and 3 + -7i |

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Evaluate this complex number square root:

√2 + 3i

Define the complex square root:

√a + bi:
root1 = x + yi
root2 = -x - yi

Calculate r:

r = √a2 + b2

r = √22 + 32

r = √4 + 9

r = √13

r = 3.605551275464

Calculate y:

y = √½(r-a)

y = √½(3.605551275464 - 2)

y = √½(1.605551275464)

y = √0.80277563773199

y = 0.89597747612984

Calculate x:

x =	b
	2y

x =	3
	2(0.89597747612984)

x =	3
	1.7919549522597

x = 1.6741492280355

Final Answer

Root 1 = 1.6741492280355 + 0.89597747612984i
Root 2 = -1.6741492280355 - 0.89597747612984i

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What is the Answer?

Root 1 = 1.6741492280355 + 0.89597747612984i
Root 2 = -1.6741492280355 - 0.89597747612984i

How does the Complex Number Operations Calculator work?

Free Complex Number Operations Calculator - Given two numbers in complex number notation, this calculator:
1) Adds (complex number addition), Subtracts (complex number subtraction), Multiplies (complex number multiplication), or Divides (complex number division) any 2 complex numbers in the form a + bi and c + di where i = √-1.
2) Determines the Square Root of a complex number denoted as √a + bi
3) Absolute Value of a Complex Number |a + bi|
4) Conjugate of a complex number a + bi
This calculator has 4 inputs.

What 6 formulas are used for the Complex Number Operations Calculator?

a + bi + (c + di) = (a + c) + (b + d)i
a + bi - (c + di) = (a - c) + (b - d)i
(a * c) + (b * c) + (a * d) + (b * d)
The square root of a complex number a + bi, is denoted as root1 = x + yi and root2 = -x - yi
|a + bi| = sqrt(a2 + b2)
a + bi has a conjugate of a - bi and a - bi has a conjugate of a + bi.

For more math formulas, check out our Formula Dossier

What 8 concepts are covered in the Complex Number Operations Calculator?

absolute valueA positive number representing the distance from 0 on a number lineadditionmath operation involving the sum of elementscomplex numbera number that can be written in the form a + b or a - bicomplex number operationsconjugateA term formed by changing the sign between two terms in a binomial.divisionseparate a number into partsmultiplicationmath operation involving the product of elementssubtractionmath operation involving the difference of elements

Example calculations for the Complex Number Operations Calculator

Complex Number Operations Calculator Video

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Square Root 2 + 3i and 3 + -7i