Answer

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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