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Earn +20 ptsQ: What are complex root?
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How do you find square root of a complex number?
This is best done if the complex number is in polar coordinates - that is, a distance from the origin, and an angle. Take the square root of the argument (the absolute value) of the complex number; and half the angle.
Can there ever be a real number root of a complex number?
Yes. They are called surds. They are also complex.
Are complex numbers closed for finding the square root of a number?
Yes. Also, for finding any other root (cubic root, fourth root, etc.). The main square root of a complex number can be found easily if it is expressed in polar notation. For example: the square root of 5 at an angle of 46 degrees) the complex number that has the absolute value 5 and an angle of 46 degrees) is equal to the square root of 5, at an angle of 46/2 = 23 degrees.
What are the sets of numbers to which the square root of -64?
Complex numbers.
Is the square root of negative 195 rational?
No, it is a complex number.
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