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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.
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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.
