Express 5-2i in polar form. Express your answer in radians to the nearest hundreth.
r=sqrt5^2+-2i^2 which equals sqrt21.Arctan of -2/5+pi equals -18.7
Polar form=sqrt21 cis -18.7
Is this correct??
To express a complex number in polar form, you need to find its modulus (r) and argument (θ).
First, let's find the modulus (r):
The modulus of a complex number is the length of the vector that represents it in the complex plane. The formula is:
r = |a + bi| = √(a^2 + b^2)
In this case, a = 5 and b = -2, so:
r = √(5^2 + (-2)^2) = √(25 + 4) = √29
Now, let's find the argument (θ):
The argument of a complex number is the angle it makes with the positive x-axis in the complex plane. The formula is:
θ = arctan(b/a)
In this case, a = 5 and b = -2, so:
θ = arctan((-2)/5) ≈ -0.38050637711 radians
Therefore, the polar form of 5-2i is:
√29 cis (-0.38050637711) = √29 * cos(-0.38050637711) + √29 * i * sin(-0.38050637711)
To express the answer in radians to the nearest hundredth, we can round -0.38050637711 to -0.38.
Thus, the correct polar form of 5-2i is:
√29 cis (-0.38)