The angle is in the 4th quadrant, so it would be either -63.43° or +296.57° (assuming your figures are correct.dylanhouse said:Homework Statement
How do I write 1-2i in polar form?
Homework Equations
The Attempt at a Solution
I know r=√5, and when using x=rcosθ, I get angle of 63.43 or 296.57. However, when I take the sin inverse of-2/√5 I get -63.43. I am really confused.
dylanhouse said:Homework Statement
How do I write 1-2i in polar form?
Homework Equations
The Attempt at a Solution
I know r=√5, and when using x=rcosθ, I get angle of 63.43 or 296.57. However, when I take the sin inverse of-2/√5 I get -63.43. I am really confused.
Polar form is a way of representing complex numbers in terms of their magnitude (distance from the origin) and angle (direction from the positive real axis). It is often written as r(cosθ + i sinθ), where r is the magnitude and θ is the angle.
To convert a complex number from rectangular form (a + bi) to polar form, you can use the formula r = √(a^2 + b^2) for the magnitude and θ = tan^-1(b/a) for the angle. Then, write the number in the form r(cosθ + i sinθ).
If you are confused about how to write a complex number in polar form, it is helpful to first identify the magnitude and angle of the number. Then, use the formula r(cosθ + i sinθ) to write it in polar form. It may also be helpful to visualize the number on the complex plane.
No, the magnitude of a complex number in polar form is always a positive value. This is because it represents the distance from the origin, which cannot be negative.
Polar form is useful for performing operations on complex numbers, such as multiplication and division, as it allows for easier manipulation of the magnitude and angle. It is also helpful for visualizing complex numbers on the complex plane and understanding their geometric properties.