Express the Complex Number -1-i in polar form.
how is complex no expressed in polar form?
what is polar form of complex no?
Please help
plot the number as a point in the x-y (real-imaginary) plane.
-1-i corresponds to (-1,-1)
That point is a distance of √2 from (0,0), and at an angle of 225° measured counterclockwise from the positive x-axis. In other words, (√2,5π/4)
The very basic nature of your question would indicate that you haven't studied the material much yet. Take a few minutes to go over it and understand the examples which are surely there.
To express a complex number in polar form, you need to represent it as a combination of two parts: the magnitude (r) and the angle (θ).
1. Magnitude (r): To find the magnitude, you can use the Pythagorean theorem. For a complex number a + bi, you need to calculate the square root of the sum of the squares of the real part (a) and the imaginary part (b). In this case, for -1 - i, the magnitude can be computed as follows:
|z| = √((-1)^2 + (-1)^2) = √(1 + 1) = √2
2. Angle (θ): The angle can be found by using the inverse tangent function. For a complex number a + bi, you can find the angle θ by taking the inverse tangent of the imaginary part divided by the real part. In this case, for -1 - i, the angle can be found as follows:
θ = atan((-1) / (-1)) = atan(1) = π/4 radians
Now that we have the magnitude (r = √2) and the angle (θ = π/4), we can express -1 - i in polar form:
-1 - i = √2*(cos(π/4) + sin(π/4))
Therefore, the polar form of -1 - i is √2cis(π/4).