Solving for the Fourth Root of i in Polar Form

Thread starter weedannycool
Start date Feb 10, 2010
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Form Polar Polar form

In summary, the fourth root of i is a complex number that can be written as ±0.7071 + ±0.7071i in rectangular form or as ±1∠±45° in polar form. Polar form is a way of representing complex numbers using magnitude and angle, typically written as r∠θ. To solve for the fourth root of i in polar form, you can use the formula (r∠θ)^1/4 = r^1/4 ∠ (θ/4). The use of ± indicates that there are two possible solutions for the fourth root of i in polar form. It can also be written in rectangular form, but polar form is often preferred for its simplicity and visual representation.

Feb 10, 2010

weedannycool

Homework Statement

evaluate i^1/4

Homework Equations

The Attempt at a Solution

don't know how to find the angle on argd

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Feb 10, 2010

Mark44

Mentor

Insights Author

What's argd? The angle for i is pi/2.

Do you know any relevant equations?

What have you tried to do?

FAQ: Solving for the Fourth Root of i in Polar Form

What is the fourth root of i?

The fourth root of i is a complex number that, when multiplied by itself four times, equals i. It is commonly written as ±0.7071 + ±0.7071i in rectangular form or as ±1∠±45° in polar form.

What is polar form?

Polar form is a way of representing complex numbers using magnitude (or distance from the origin) and angle. It is typically written as r∠θ, where r is the magnitude and θ is the angle in degrees or radians.

How do you solve for the fourth root of i in polar form?

To solve for the fourth root of i in polar form, you can use the formula (r∠θ)^1/4 = r^1/4 ∠ (θ/4). This means you take the fourth root of the magnitude and divide the angle by 4. This will give you the two possible solutions ±r^1/4 ∠ (θ/4).

Why is ± used when writing the fourth root of i in polar form?

The use of ± indicates that there are two possible solutions for the fourth root of i in polar form, as complex numbers have two roots. This is similar to how the square root of a positive number can have a positive or negative solution.

Can the fourth root of i be written in rectangular form?

Yes, the fourth root of i can also be written in rectangular form as ±0.7071 + ±0.7071i. This is because rectangular and polar forms are two different ways of representing the same complex number. However, polar form is often preferred for its simplicity and visual representation of the magnitude and angle.