the imaginary i or j which is ewuivalent to square root of -1 has a phase difference of ____ with real number 1. what's the answer? 0,45,90,180, or 360? and why?
hint:
1 is on the +x-axis
i is on the +y-axis.
How far do you have to rotate the +x direction to point in the +y direction?
i don't know there are given choices of a.) 0 degrees, along or within the force. b.)90 degrees. c.) 360 degrees, one complete revolution d.) 180 degrees. e.) 45 degrees, horizontal and vertical component or equal
oh, come on. You can draw x- and y-axes, surely? They meet at a right angle. How many degrees is that?
Just place a pencil pointing out the +x axis, and rotate it till it points upward along the y-axis. You must surely know how many degrees that is. If not, you are in for a bumpy ride.
To determine the phase difference between the imaginary number i (or j) and the real number 1, we need to understand the concept of phase difference and its relation to complex numbers.
Phase difference is a measure of the angular displacement between two quantities, typically expressed in degrees (°) or radians (rad). In the context of complex numbers, the phase difference represents the angular displacement of the complex number when plotted on the complex plane.
In this case, to find the phase difference between the imaginary number i (or j) and the real number 1, we can consider the polar form of complex numbers. The polar form of a complex number is given as:
z = r * (cos θ + i*sin θ),
where r represents the magnitude of the complex number, and θ represents the phase angle or argument.
Since i (or j) is equal to the square root of -1, we can write it as i = √(-1).
For the real number 1, we can represent it as 1 = 1 * (cos 0° + i*sin 0°).
Now, let's find the phase angle (θ) of i (or j) by expressing it in polar form:
i = √(-1) = 1 * (cos 90° + i*sin 90°).
Therefore, the phase angle (θ) of i (or j) is 90°.
The phase difference is then calculated by subtracting the phase angle of the real number 1 from the phase angle of i (or j):
Phase difference = Phase angle of i (or j) - Phase angle of 1
= 90° - 0°
= 90°.
So, the answer to the question is 90°.