Enter a and bi piece:

a =  bi =

Enter c and di piece:

c =  di =
              

Answer
Success!
Conjugate of 2 + 3i = 2 - 3i

↓Steps Explained:↓

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

Evaluate this complex number absolute value

|2 + 3i|

Define the complex absolute value:

On the number line
Distance from 0 to that number. |a + bi| = √a2 + b2

Given a = 2 and b = 3, we have:

|2 + 3i| = √a2 + b2

|2 + 3i| = √22 + 32

|2 + 3i| = √4 + 9

|2 + 3i| = √13

Determine the complex conjugate for

2 + 3i

Define the complex conjugate:

The conjugate of a + bi = a - bi

Final Answer

Conjugate of 2 + 3i = 2 - 3i
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Related Calculators:  Fractions and Mixed Numbers  |  Order of Operations  |  Base Conversion Operations



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