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The set of real numbers are a subset of the set of complex numbers: imagine the complex plane with real numbers existing on the horizontal number line, and pure imaginary existing on the vertical axis. The entire plane (which includes both axes) is the set of complex numbers. So any real number (such as pi) will also be a complex number. But many people think of complex numbers as something that is "not a real number".
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What is -4 in standard form as an complex number?
-4=4ei*pi
What is the number for pi on a calculator?
Most complex calculators have pi built into it. But you can use 3.14 if you only have a four function calc.
How can you square a complex number in trigonometric form?
Multiply the angle by 2, and square the magnitude. The angle can be rewritten between (-180° & +180°) (or -pi and +pi radians), after multiplying.
What is the additive inverse of a complex number?
Just change the sign of both the real part, and the imaginary part. For instance, the additive inverse of:3-4i is: -3+4i (If you have the complex number in polar coordinates, add or subtract pi to the angle.)
What is the largest amount of pi that you can think of?
If you mean the number pi, you can't have a "large amount of pi" or a "small amount of pi" - the number pi will always be the number pi (approximately 3.1416).
What is -4 in standard form as an complex number?
-4=4ei*pi
Is pi irrational rational complex or an integer?
pi is real, irrational and transcendent; it is not rational, complex, nor an integer.Yes, it is non-terminating and non-repeating.Yes, pie is an irrational number.
What is the number for pi on a calculator?
Most complex calculators have pi built into it. But you can use 3.14 if you only have a four function calc.
What complex number lies below the real axis and to the right of the imaginary axis?
Complex numbers whose polar representation is (r, theta) where 3*pi/2 < theta < 2*pi.
Pi is transcendental What does this mean in mathematics?
An algebraic number is one which is a root of a non-constant polynomial equation with rational coefficients. A transcendental number is not an algebraic number. Although a transcendental number may be complex, Pi is not.
How can you square a complex number in trigonometric form?
Multiply the angle by 2, and square the magnitude. The angle can be rewritten between (-180° & +180°) (or -pi and +pi radians), after multiplying.
Why you restrict the argument of a complex number between -pi and pi?
Because the trigonometric functions (sine and cosine) are periodic, with period 2*pi. If the argument were not restricted, you would have an infinite number of answers. You could, of course, restrict the argument to any interval of size 2*pi: 3.5pi to 5.5pi, for example.
Definition of principle square root?
The square root of a positive real number can either be +/-. The principle square root is defined as the positive value. sqrt(9) is +/- 3, but the principle square root of 9 is 3. For complex numbers the principle square root is the argument (or angle) of the complex number that lies between (-pi,pi]. I am pretty sure that the upper angle pi is closed while the lower angle -pi is open, but not 100%.
What does it mean for a number to be transcendental?
An algebraic number is a number that is a root of a non-zero polynomial with rational coefficients. A transcendental number is a real or complex number that is not an algebraic number. Two notable examples are pi and e.
What is the additive inverse of a complex number?
Just change the sign of both the real part, and the imaginary part. For instance, the additive inverse of:3-4i is: -3+4i (If you have the complex number in polar coordinates, add or subtract pi to the angle.)
What is the largest amount of pi that you can think of?
If you mean the number pi, you can't have a "large amount of pi" or a "small amount of pi" - the number pi will always be the number pi (approximately 3.1416).
What can be a non rational number?
It can be a real number which is not a rational number. That is, an irrational number such as sqrt(2), or cuberoot(5), or pi, or e, or phi. Or it can be a number that is not even a real number, such as a complex number or a quaternion.
