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Euler form of complex number, Properties of argument of a complex number is considered one of the most asked concept.
21 Questions around this concept.
Let be complex numbers such that and arg Then arg equals:
The polar form of complex number z = r (cos ? + i sin ?)
In Euler form (cos ? + i sin ?) part of the polar form of complex numbers is represented by eiΘ. So, z = r (cos ? + i sin ?) is written as r.eiΘ in Euler's Form
We know the expansion of ex is
So, ei? = cos? + isin? and
e-i? = cos? - isin?
Euler forms make algebra very simple for complex numbers in cases where multiplication, division or powers of complex numbers are involved. Any complex number can be expressed as
Application of Euler form:
1. Multiplication of two complex numbers:
2. Division also can be done in the same way,
3. The logarithm of Complex Number
Value of k should be chosen in such a way that arg lies between (-?,?]
This formula for argument can be generalised for n number of complex in similar way
where k is an integer
k belongs to an integer
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