# What is the polar form of -2^i?

• KyleS4562
In summary, to convert -2^i to polar and rectangular form, we can use the properties of logarithms to rewrite the number as 2^i and then use the polar form equation mag(a+ib)=sqrt(a^2+b^2) to find the magnitude and the exponential form equation exp(i*angle)=cos(angle)+i*sin(angle) to find the angle. We can also use the rectangular form equation 2=exp(ln2) to find the rectangular form.
KyleS4562

## Homework Statement

Convert -2^i to polar and rectangular form

## Homework Equations

mag(a+ib)=sqrt(a^2+b^2)

exp(i*angle)=cos(angle)+i*sin(angle)

## The Attempt at a Solution

im not sure how to get the polar (or rectangular form) of -2^i.
i know the answer is exp(-2.448rad)... i just don't know the property that allows me to get there or to the rectangular form

Last edited:
Use the properties of logarithms to convert the 2 into a power of e, ie.
$$2 = e^{something}$$
(And yes, I know that 2 is negative. Let's not worry about it right now.)

i see wat to do now... thank you... it would be 2=exp(ln2) which means 2^i=exp(ln(2^i))=exp(i*ln(2)) which is polar form... totally forgot the properties of log

By $-2^i$ do you mean $-(2^i)$ or $(-2)^i$. They are different numbers.

## 1. What is the polar form of -2^i?

The polar form of a complex number is a way of expressing it in terms of its magnitude (or modulus) and angle (or argument). For -2^i, the polar form is written as 2e^(iπ/2).

## 2. How is the polar form of a complex number calculated?

The polar form of a complex number can be calculated using the following formula: r(cosθ + i sinθ), where r is the magnitude of the number and θ is the angle in radians.

## 3. What is the difference between polar form and rectangular form of a complex number?

The rectangular form of a complex number is written as a + bi, where a and b are real numbers and i is the imaginary unit. In contrast, the polar form is expressed as r(cosθ + i sinθ), where r is the magnitude and θ is the angle.

## 4. How is the angle determined in the polar form of a complex number?

The angle in the polar form of a complex number is determined by finding the angle between the positive real axis and the line connecting the origin to the complex number in the complex plane. This angle is usually measured in radians.

## 5. Can negative numbers be written in polar form?

Yes, negative numbers can also be written in polar form. The magnitude would still be a positive number, and the angle would be 180 degrees (or π radians) more than the angle for the positive number with the same magnitude.

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