- #1
naspek
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Let z = 4e^i(pi/6)
find iz and |e^iz|
what is iz?
is it imaginary part of z?
find iz and |e^iz|
what is iz?
is it imaginary part of z?
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.
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?naspek said:what bout the second part?
The exponential form of a complex number is written as re^{iθ}, where r is the magnitude or modulus of the complex number and θ is the angle or argument in radians.
To convert a complex number from rectangular form a + bi to exponential form re^{iθ}, you can use the following formula: r = √(a^{2} + b^{2}) and θ = tan^{-1}(b/a), where a and b are the real and imaginary parts of the complex number, respectively.
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.
The polar form of a complex number is another name for the exponential form, written as re^{iθ}, where r is the modulus and θ is the argument.
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.