I posted earlier and didn't get an answer so I'm posting again-hoping someone could please check these two-I think they're correct
Please check my answer: I think it's correct?
1.Find polar form of (-3,2)
r=sqrt of (-3)^2 + 2^2)=sqrt (13) = 3.61
tan^-1(2/-3) = 33.79
180-33.79 = 146.31degrees
polar points are (sqrt13,146.31degrees)
2. Rectangular form of (3,112degrees)
3cos112= (-1.12)
3sin112=2.78
rectangular points are(-1.12,2.78)
Thanks for checking
To verify your answers, let's go through the steps to find the polar form of (-3,2) and the rectangular form of (3,112 degrees).
1. Polar Form of (-3,2):
To find the polar form of a complex number, we need to convert it from rectangular form (a+bi) to polar form (r∠θ), where r is the magnitude and θ is the angle.
a. Calculate the magnitude (r):
The magnitude of a complex number is found using the distance formula: r = √(a^2 + b^2)
In this case, r = √((-3)^2 + 2^2) = √(9 + 4) = √13 ≈ 3.61
b. Calculate the angle (θ):
The angle can be determined using the arctan function: θ = tan^(-1)(b/a)
In this case, θ = tan^(-1)(2/-3) ≈ -33.69 degrees (note: rounded to two decimal places).
c. Adjust the angle to the polar coordinate system:
Since the given angle is in the fourth quadrant, we need to add 180 degrees to it to get the angle in the polar coordinate system.
θ' = θ + 180 = -33.69 + 180 = 146.31 degrees
Therefore, the polar form of (-3,2) is (√13, 146.31 degrees).
2. Rectangular Form of (3,112 degrees):
To find the rectangular form of a complex number given in polar form (r∠θ), we use the formulas:
a = r * cos(θ) and b = r * sin(θ), which represent the real and imaginary parts of the complex number, respectively.
a. Calculate the real part:
a = 3 * cos(112 degrees) ≈ -1.12 (rounded to two decimal places)
b. Calculate the imaginary part:
b = 3 * sin(112 degrees) ≈ 2.78 (rounded to two decimal places)
Therefore, the rectangular form of (3,112 degrees) is approximately (-1.12, 2.78).
Based on the explanations provided above, please compare your answers with the correct responses.