Assertion: complex number | /r/HasProperty | equal
Facets:
value: to its complex conjugate
type: OTHER
value: to 0
type: OTHER
value: to 1
type: OTHER
value: re ⁡
type: OTHER
Source sentences:
text: Two complex numbers are equal if and only if both their real and imaginary parts are equal.
text: That is, complex numbers z 1 {\displaystyle z_{1}} and z 2 {\displaystyle z_{2}} are equal if and only if Re ⁡ ( z 1 ) =
text: Now, if two complex numbers are equal, then their real parts have to be equal and their imaginary parts have to be equal.
text: First, if the magnitude of a complex number is 0, then the complex number is equal to 0.
text: (We leave it to the reader to verify that any non-zero complex number divided by itself is in fact equal to 1.)
text: To be equal, two complex numbers must have equal real parts and equal imaginary parts.
text: From this, it is obvious that two complex numbers (a+bi) and (c+di) are equal if and only if a=c and b=d, that is, the real and imaginary components are equal.
text: Based on this formula, one can expect that the-th root of the complex numberis equal toThis is true that the complex number, raised to degree n, is equal toBut
text: This number is called imaginary because it is equal to the square root of negative one.
text: Problem : What complex number is equal to its complex conjugate?