Enter a and bi piece:

a =  bi =

Enter c and di piece:

c =  di =
              

Answer
Success!
Root 1 = 1.4704685172313 + 2.0401660864176i
Root 2 = -1.4704685172313 - 2.0401660864176i

↓Steps Explained:↓

Evaluate this complex number square root:

√-2 + 6i

Define the complex square root:

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

Calculate r:

r = √a2 + b2

r = √-22 + 62

r = √4 + 36

r = √40

r = 6.3245553203368

Calculate y:

y = √½(r-a)

y = √½(6.3245553203368 - -2)

y = √½(8.3245553203368)

y = √4.1622776601684

y = 2.0401660864176

Calculate x:

x  =  b
  2y

x  =  6
  2(2.0401660864176)

x  =  6
  4.0803321728351

x = 1.4704685172313

Final Answer

Root 1 = 1.4704685172313 + 2.0401660864176i
Root 2 = -1.4704685172313 - 2.0401660864176i
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Related Calculators:  Fractions and Mixed Numbers  |  Order of Operations  |  Base Conversion Operations


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