Modulus Complex Number
Introduction:
In this article we are going to see a lot about the modulus of complex numbers. The complex number modulus important to calculate complex coordinate system it becomes the modulus value of the complex numbers. All the complex numbers are expressed with the letter i. By knowing the properties the value i we can simplify the relations involving complex numbers.
Modulus of complex number:
A complex number has two parts namely the real part and the imaginary part. The general notation of complex number is given by the equation a + bi,
Where a and b are all real numbers. And i is the imaginary unit.
The absolute value or the modulus complex number is given by the formula sqrt(a2 + b2). We have to note that while calculating the modulus of complex numbers i is omitted from formula for calculating the modulus value. Also other properties of i are given by
i2 = -1
i3 = - i
Also the above values can be used foe the calculation involving the complex numbers. In simple words the modulus of a complex number is the square root of the sum of the squares of real coefficient and imaginary coefficient.
Example Problems on modulus complex number :
1. Calculate the modulus of complex number 5+4i.
Solution: Formula for modulus complex number x +iy = (x2+y2).
= √ (52+42)
= √ (25+16)
= √ (41)
Modulus of complex number = √ (41)
2. Calculate the modulus of complex number 4+3i.
Solution: Formula for modulus complex number x +iy = (x2+y2).
= √ (42+32)
= √ (16+9)
= √(25).
Modulus of complex number = 5
3. Calculate the modulus of complex number 6+8i.
Solution: Formula for modulus complex number x +iy = (x2+y2).
= √ (62+82)
= √ (36+64)
= √(100).
Modulus of complex number = 10
Practice problems on modulus complex number:1. Calculate the modulus of complex number 3+9i.
Answer: Modulus of complex number = √(90).
2. Calculate the modulus of complex number 4+8i.
Answer: Modulus of complex number = √(80) = 4√(5)
In this article we are going to see a lot about the modulus of complex numbers. The complex number modulus important to calculate complex coordinate system it becomes the modulus value of the complex numbers. All the complex numbers are expressed with the letter i. By knowing the properties the value i we can simplify the relations involving complex numbers.
Modulus of complex number:
A complex number has two parts namely the real part and the imaginary part. The general notation of complex number is given by the equation a + bi,
Where a and b are all real numbers. And i is the imaginary unit.
The absolute value or the modulus complex number is given by the formula sqrt(a2 + b2). We have to note that while calculating the modulus of complex numbers i is omitted from formula for calculating the modulus value. Also other properties of i are given by
i2 = -1
i3 = - i
Also the above values can be used foe the calculation involving the complex numbers. In simple words the modulus of a complex number is the square root of the sum of the squares of real coefficient and imaginary coefficient.
Example Problems on modulus complex number :
1. Calculate the modulus of complex number 5+4i.
Solution: Formula for modulus complex number x +iy = (x2+y2).
= √ (52+42)
= √ (25+16)
= √ (41)
Modulus of complex number = √ (41)
2. Calculate the modulus of complex number 4+3i.
Solution: Formula for modulus complex number x +iy = (x2+y2).
= √ (42+32)
= √ (16+9)
= √(25).
Modulus of complex number = 5
3. Calculate the modulus of complex number 6+8i.
Solution: Formula for modulus complex number x +iy = (x2+y2).
= √ (62+82)
= √ (36+64)
= √(100).
Modulus of complex number = 10
Practice problems on modulus complex number:1. Calculate the modulus of complex number 3+9i.
Answer: Modulus of complex number = √(90).
2. Calculate the modulus of complex number 4+8i.
Answer: Modulus of complex number = √(80) = 4√(5)