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Not necessarily. It can be wholly imaginary.
For example, 1 + i actually has two complex conjugates. Most schools will teach you that the complex conjugate is 1 - i. However, -1 + i is also a conjugate for 1 + i. (Their product is -1 times the product of the "normal" conjugate pair).
The sum of 1 + i and -1 + i = 2i
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Is the sum of a complex number and its conjugate a real or imaginary number?
Their sum is real.
Conjugate and a complex number equal?
The conjugate will have equal magnitude. The angle from the real axis will be the same angle measure (but opposite direction).
What is the sum of two complex conjugate number?
Since the imaginary parts cancel, and the real parts are the same, the sum is twice the real part of any of the numbers. For example, (5 + 4i) + (5 - 4i) = 5 + 5 + 4i - 4i = 10.
How is a complex number defined?
A complex number is a two-dimensional continuous quantity that is the sum of a real number and an imaginary number expressed in the form a+bi and plotted on a complex coordinate plane with the real line on the horizontal x-axis and the imaginary line on the vertical y-axis.
What two integers have a product of 24 and a sum of 5?
The complex conjugate pair 2.5 - i*0.5*sqrt(71) and 2.5 + i*0.5*sqrt(71) where i is the imaginary number representing the square root of -1.
