0
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
Add your answer:
Earn +20 pts
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.
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).
The sum of a complex number and its conjugate?
Given a complex number z = a + bi, the conjugate z* = a - bi, so z + z*= a + bi + a - bi = 2*a. Note that a and b are both real numbers, and i is the imaginary unit: +sqrt(-1).
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.
The sum of two complex numbers is always a complex number?
A "complex number" is a number of the form a+bi, where a and b are both real numbers and i is the principal square root of -1. Since b can be equal to 0, you see that the real numbers are a subset of the complex numbers. Similarly, since a can be zero, the imaginary numbers are a subset of the complex numbers. So let's take two complex numbers: a+bi and c+di (where a, b, c, and d are real). We add them together and we get: (a+c) + (b+d)i The sum of two real numbers is always real, so a+c is a real number and b+d is a real number, so the sum of two complex numbers is a complex number. What you may really be wondering is whether the sum of two non-real complex numbers can ever be a real number. The answer is yes: (3+2i) + (5-2i) = 8. In fact, the complex numbers form an algebraic field. The sum, difference, product, and quotient of any two complex numbers (except division by 0) is a complex number (keeping in mind the special case that both real and imaginary numbers are a subset of the complex numbers).
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.
Which number belongs to the set of complex numbers?
Lots of numbers do. To begin, all real numbers do. Multiples of sqrt(-1), aka. imaginary numbers, do. The Complex Numbers are all numbers which are the sum of a real number and an imaginary number.
What is multiplied to get 420 but has a sum of 14?
The complex conjugate pair 7 - 19.261i and7 + 19.261iwhereiis the imaginary square root of -1.
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.
What is a A Non-Real number?
Most famously, an imaginary number, that is, a number whose square (which is the number multiplied by itself) is negative. All real numbers have positive squares. A complex number, is a number which is the sum of a real number and an imaginary number, and so is also a non-real number.
What two numbers have a sum of 6 and difference of 0.3?
0.15 - 2.44489i and its complex conjugate, 0.15 + 2.44489i where i is the imaginary square root of -1.
What 2 numbers have the product of 7000 and the sum of 55?
The two numbers are the complex conjugate pair27.5 - 79.0174iand27.5 + 79.0174iwhere i is the imaginary square root of -1.
