5(sqrt3-5i) in polar form.
my book has a lot of typos and misprints and this could be one.
Is the answer 10(cos(5pi/3)+isin(5pi/3))
ps. bobpursley you're coming off as a little mean and its really not necessary. I tried to do what you said yesterday but I don't have my scientific calculator with me and I can't find one online that I can use.
Thanks.)
i have the same book you do (at least i'm pretty sure) and i can't figure this out either. If you did find the answer, please help.
To express a complex number in polar form, we need to find its magnitude (r) and argument (theta). The magnitude of a complex number is given by the formula:
r = sqrt(x^2 + y^2)
where x and y are the real and imaginary parts of the complex number, respectively. In this case, x = 5sqrt(3) and y = -5.
r = sqrt((5sqrt(3))^2 + (-5)^2)
r = sqrt(75 + 25)
r = sqrt(100)
r = 10
Next, we need to find the argument (theta) of the complex number. We can use the formula:
theta = arctan(y / x)
theta = arctan(-5 / (5sqrt(3)))
theta = arctan(-1 / sqrt(3))
theta = arctan(-sqrt(3) / 3)
Now, let's evaluate the value of theta.
theta ≈ -0.5236 rad (approximately -pi/6)
Since theta is negative, we need to add 2pi to it to bring it to the standard range of 0 to 2pi.
theta ≈ -0.5236 + 2pi ≈ 5.7596 rad (approximately 5pi/3)
Now, we can express the complex number in polar form:
5(sqrt(3) - 5i) = 10(cos(5pi/3) + isin(5pi/3))
So, your answer of 10(cos(5pi/3) + isin(5pi/3)) is correct.