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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.
How do you find the perimeter and area for complex shapes without a grid?
To find the perimeter and areas of complex shape without a grid you should divide the shape into simple shapes and find the area of each shape alone and then add up the areas all together to get the area of the whole shape. Example: If there is a shape that can be divided into 2 triangles and 1 rectangle then you will find the area of each triangle alone and then the area of the rectangle then add up all the areas together.
How do you find out the domain of x squared?
You can square any real number (complex ones too) so the domain is all real numbers.
What is the need for complex numbers?
The square of any real number cannot be negative. However, there are equations whose solutions require the square root of negative numbers. The real number system was extended to the set of complex number to allow such operations. In some ways, this is analogous to the set of integers being extended to the set of rational numbers to allow division (when the denominator was not a factor of the numerator), or the set of rational numbers being extended to real numbers to allow square (and other) roots.
Explain why it is not possible to take a square root of a negative number?
Actually, it is. It just depends within what set you are doing your calculation, that is, what do you consider an "acceptable solution". The question of the square root means, which number, when squared, gives a specific number. Within the real numbers, the square of a positive number is positive, the square of a negative number is also positive. Therefore, there are no real numbers whose square is negative. Within the complex numbers, the square root of -1, for example, is i (the "imaginary unit") - that is, i2 = -1. Similarly, the square root of -4 is 2i, the square root of -9 is 3i, the square root of -2 is (square root of 2 times i), etc. In some areas, complex numbers are acceptable as solutions, in other areas, they are not. In the same vein, negative numbers are acceptable as solutions to certain problems, but not for certain other problems.
