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
Common Core State Standards In This Lesson
HSN.CN.A.2, HSN.CN.A.3
What is the Answer?
Conjugate of 2 + 3i = 2 - 3i
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.
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.
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.
What 8 concepts are covered in the Complex Number Operations Calculator?
- absolute value
- A positive number representing the distance from 0 on a number line
- addition
- math operation involving the sum of elements
- complex number
- a number that can be written in the form a + b or a - bi
- complex number operations
- conjugate
- A term formed by changing the sign between two terms in a binomial.
- division
- separate a number into parts
- multiplication
- math operation involving the product of elements
- subtraction
- math operation involving the difference of elements
