How do you convert degrees to radians?
what's the modulus and the principle argument (complex n°)
To convert degrees to radians, you need to multiply the degree value by π/180. The conversion formula is as follows:
Radians = Degrees * π/180
Here’s an example to convert 45 degrees to radians:
Radians = 45 * π/180
= π/4
Therefore, 45 degrees is equal to π/4 radians.
Now, let's move on to your second question about the modulus and principal argument in complex numbers.
Modulus:
In complex numbers, the modulus (also known as the absolute value or magnitude) represents the distance between the origin (0,0) and the point on the complex plane. To find the modulus of a complex number (a + bi), the formula is:
Modulus = sqrt(a² + b²)
For example, let's find the modulus of the complex number 3 + 4i:
Modulus = sqrt(3² + 4²)
= sqrt(9 + 16)
= sqrt(25)
= 5
Therefore, the modulus of 3 + 4i is 5.
Principal Argument:
The principal argument is the angle (measured in radians) between the positive real axis and the line connecting the origin to the point on the complex plane. To find the principal argument of a complex number (a + bi), the formula is:
Principal Argument = arctan(b/a)
Note: When calculating the principal argument, make sure to consider the signs of a and b to determine the correct quadrant.
For example, let's find the principal argument of the complex number 3 + 4i:
Principal Argument = arctan(4/3)
≈ 0.93 radians
Therefore, the principal argument of 3 + 4i is approximately 0.93 radians.