Write 1-2i in Polar Form - Solve Confusion

• dylanhouse
In summary, to write 1-2i in polar form, you can use the formula x=rcosθ and solve for the angle using inverse trigonometric functions. In this case, the angle would be in the 4th quadrant, either -63.43° or +296.57°. It is important to keep track of the signs of the imaginary and real parts to ensure the correct quadrant is chosen.
dylanhouse

Homework Statement

How do I write 1-2i in polar form?

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?

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.
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?

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.

The formula is arc tan (Im part)/(Real part). You need to keep track of the numerator and denominator signs to make sure you land in the correct quadrant. In other words, the fact that the I am is - and the Re is + tells you which quadrant to land in.

1. What is polar form in mathematics?

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.

2. How do I convert a complex number from rectangular form to polar form?

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).

3. How do I solve confusion when writing a complex number in polar form?

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.

4. Can a complex number have a negative magnitude in polar form?

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.

5. What is the purpose of using polar form to represent complex numbers?

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.

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