0
A complex number, z, may be written as z = x + iy where x and y are real and i is the imaginary square root of -1.
x is the real part of z and iy is its imaginary part.
The Argand diagram for z would show it as if it had the coordinates (x, y) in the Cartesian plane. However, where the Cartesian plane has the x-axis the Argand diagram has the real part, and where the Cartesian plane has the y-axis the Argand diagram has the imaginary part.
Equivalently, z can be defined in terms of polar coordinates: z = (r, q).
This is the same as z = rcosq + i*rsinq, so the real part is rcosq.
Add your answer:
Earn +20 pts
How can you tell which part of a complex number is the real part and which is the imaginary part?
The imaginary part is expressed as a product of i(square root of negative one), typically following a plus sign, so that the complex number has the form a + bi, with "a" the real part and "bi" the imaginary part.
Are imaginary and complex numbers the same?
No. A complex number is a number that has both a real part and an imaginary part. Technically, a pure imaginary number ... which has no real part ... is not a complex number.
Is 4 a complex number?
A complex number is denoted by Z=X+iY, where X is the real part and iY is the imanginary part. So the number 4 would be 4+i0 and is the real part of a complex number and so 4 by itself is just a real number, not complex.
Can a number be both complex and imaginary?
A complex number has a real part and a (purely) imaginary part, So imaginary numbers are a subset of complex numbers. But the converse is not true. A real number is also a member of the complex domain but it is not an imaginary number.
How do you write complex numbers in the form a plus bi?
A complex number comes in two parts: a real part and an imaginary part. If the value of the real part is a and the value of the imaginary part is b, the number is written as a + bi.
How can you tell which part of a complex number is the real part and which is the imaginary part?
The imaginary part is expressed as a product of i(square root of negative one), typically following a plus sign, so that the complex number has the form a + bi, with "a" the real part and "bi" the imaginary part.
Are imaginary and complex numbers the same?
No. A complex number is a number that has both a real part and an imaginary part. Technically, a pure imaginary number ... which has no real part ... is not a complex number.
Is 4 a complex number?
A complex number is denoted by Z=X+iY, where X is the real part and iY is the imanginary part. So the number 4 would be 4+i0 and is the real part of a complex number and so 4 by itself is just a real number, not complex.
Is every complex nberan imaginary number?
No. A complex number consists of a real part and a imaginary part. If the real part equals zero, there is only the imaginary left and you could therefor argue that it is an imaginary number (or else it would still be a complex number -with a real part=0)
A number can be both real and complex?
Any real number is a complex number with an imaginary part equal to 0
A complex number might not be a pure imaginary number?
True. Complex numbers have a real part and an imaginary part. If either one of these is zero, the complex number will be a pure real or a pure imaginary.
Is every complex number a real number?
A complex number z has two parts - a real part and an imaginary part - and is of the form:z := x + iywherex and y are real numbersi represents √-1, that is i2 = -1.("x" is the real part, "iy" is the imaginary part)As x and y are real numbers, they can be any real number including 0.If x = 0, the resulting complex number z is of the form "iy" and is totally imaginary;if y = 0, the resulting complex number z is of the form "x" and is totally real.Thus real numbers are a subset of complex numbers, that is every real number is a complex number, but not every complex number is a real number.yes
Can a number be both complex and imaginary?
A complex number has a real part and a (purely) imaginary part, So imaginary numbers are a subset of complex numbers. But the converse is not true. A real number is also a member of the complex domain but it is not an imaginary number.
How do you write complex numbers in the form a plus bi?
A complex number comes in two parts: a real part and an imaginary part. If the value of the real part is a and the value of the imaginary part is b, the number is written as a + bi.
How can you simplify a complex fraction?
Multiply top and bottom by the complex conjugate of the bottom complex number; this will make the bottom complex number into a real number which can then be made into fractions and simplified with the real part and the imaginary part (the multiplier of i [√-1]) of the multiplied out top number.
Fomular for complex numbers?
A complex number is a number with a real part and an imaginary part. It is written in the form a+bi. a is the real part & bi is the imaginary part. Recall that i = square root of -1. An example would be 2+3i.
Why complex no is denoted by z?
There are no real reason why it is denoted by z, but that the real number axis is denoted by x, imaginary number is denoted by y, the real part of a complex number is denoted by a, the imaginary part of a complex number is denoted by b, so there is z left.
