# Complex number(exponential form)

• naspek
In summary, z = 4e^i(pi/6) and it is being asked to find iz and |e^iz|. "iz" is i times z, but z is in polar form while i is in rectangular form. To solve this, either express i in polar form or z in rectangular form and then multiply them together. The second part involves finding the absolute value of e^iz.
naspek
Let z = 4e^i(pi/6)
find iz and |e^iz|

what is iz?
is it imaginary part of z?

No, "iz" is exactly what it looks like: i times z. The difficulty appears to be that z is in polar form while i is in "rectangluar" form. Either write i in polar form or write z in rectangular form. Then multiply.

HallsofIvy said:
No, "iz" is exactly what it looks like: i times z. The difficulty appears to be that z is in polar form while i is in "rectangluar" form. Either write i in polar form or write z in rectangular form. Then multiply.

what bout the second part?

naspek said:
what bout the second part?
That was what I meant when I said "Either write i in polar form or write z in rectangular form. Then multiply." What is i in polar form? What is z in rectangular form?

## 1. What is the exponential form of a complex number?

The exponential form of a complex number is written as re, where r is the magnitude or modulus of the complex number and θ is the angle or argument in radians.

## 2. How do you convert a complex number from rectangular form to exponential form?

To convert a complex number from rectangular form a + bi to exponential form re, you can use the following formula: r = √(a2 + b2) and θ = tan-1(b/a), where a and b are the real and imaginary parts of the complex number, respectively.

## 3. How do you perform arithmetic operations on complex numbers in exponential form?

To add or subtract complex numbers in exponential form, you can simply add or subtract the magnitudes and add or subtract the angles. To multiply complex numbers in exponential form, you can multiply the magnitudes and add the angles. To divide complex numbers in exponential form, you can divide the magnitudes and subtract the angles.

## 4. What is the polar form of a complex number?

The polar form of a complex number is another name for the exponential form, written as re, where r is the modulus and θ is the argument.

## 5. What is the significance of the imaginary unit i in exponential form?

The imaginary unit i is used to represent the square root of -1 in exponential form. It is necessary for representing the imaginary part of a complex number and allows us to perform calculations with complex numbers using the same rules as real numbers.

• Calculus and Beyond Homework Help
Replies
7
Views
1K
• Calculus and Beyond Homework Help
Replies
12
Views
1K
• Calculus and Beyond Homework Help
Replies
13
Views
1K
• Calculus and Beyond Homework Help
Replies
7
Views
1K
• Calculus and Beyond Homework Help
Replies
3
Views
1K
• Calculus and Beyond Homework Help
Replies
22
Views
2K
• Calculus and Beyond Homework Help
Replies
10
Views
1K
• Calculus and Beyond Homework Help
Replies
5
Views
892
• Calculus and Beyond Homework Help
Replies
6
Views
3K
• Calculus and Beyond Homework Help
Replies
3
Views
1K