write the complex number -5 in polar form.
I don't get how to do this because arctan of b/a would be 5/0 which is a fraction with no solution. Also, is a zero? Sorry if I'm being confusing! Thank you!
arc tan of 5/0 might be arc tan 90 degrees ? Draw y value of 5 and x value of almost 0 and look at the angle :)
To express a complex number in polar form, we need to find its magnitude (r) and angle (θ) in the polar plane.
In this case, we have the complex number -5, which can be written as -5 + 0i. To find the magnitude, we can use the formula:
r = sqrt(a^2 + b^2)
where a is the real part (-5) and b is the imaginary part (0). In this case, we have:
r = sqrt((-5)^2 + 0^2)
= sqrt(25 + 0)
= sqrt(25)
= 5
So, the magnitude (r) of the complex number -5 is 5.
Next, we need to find the angle (θ) in the polar plane. The angle can be determined using the inverse tangent (arctan) function:
θ = arctan(b/a)
However, this formula is not applicable in this case because a is equal to -5 and b is equal to 0, which results in a division by zero situation (5/0). This is where it gets a bit trickier.
When the real part (a) is negative, as in this case, we need to consider the angle relative to the negative real axis. By convention, we can set the angle (θ) for -5 to be π (pi) radians or 180 degrees, which is equivalent to going straight down from the origin in the polar plane.
Thus, the polar form of the complex number -5 is:
-5 = 5 * (cos(π) + i * sin(π))
In polar form, the magnitude 5 (r) is multiplied by the angle π (θ) in the complex plane.