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Since a sinusoidal waveform is really based off of a rotating circle you can describe its position in time using polar coordinates (magnitude, phase angle) OR put that circle on a Cartesian plane and describe it with normal x and y coordinates (instead of x and y we call it real and imaginary because the sinusoids we see are really just the up and down parts, aka 1 of the 2 dimensions, of the entire rotating circle).
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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 5192716162 a real number?
Real numbers are the subset of complex numbers with the property that their imaginary part is zero. Since the above number has no imaginary part, it is a real number.
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.
What is the square root of -34?
Square roots of negative numbers are complex, meaning that they carry a 'real' and an 'imaginary' part. Here the real part is approximately 5.8309518948453 and the imaginary part is i.
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.
