- #1
brandy
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would in = an infinite amount of real possibilites if n is complex. considering that 1+0i is still a complex number, or is that wrong?
brandy said:i just asked if it would have an infinite amount of possibilites, obviously i have already thought about this and already know some examples of how it will be real. its a yes or no + justification response.
im using De Moirve's theorm and i can already prove that i^i is real. and hence i^ai is real even if its complex and if n=ai+c it will be real if c is an even number or o.
the other part of my question was, can i acurately say that a+0i is a complex number?
A complex number is a number that can be written in the form a + bi, where a and b are real numbers and i is the imaginary unit (√-1).
The value of i^n depends on the value of n. If n is an even integer, i^n will be a real number. If n is an odd integer, i^n will be an imaginary number. If n is a non-integer or negative, the value of i^n will also be complex.
The values of n that make i^n real are even integers such as 2, 4, 6, etc. For these values, i^n will be equal to 1, -1, 1, etc. respectively.
No, i^n cannot be both real and imaginary. It can only be one or the other, depending on the value of n.
Complex numbers are used in various fields of science, such as engineering, physics, and mathematics. They are particularly useful in solving problems involving electrical circuits, quantum mechanics, and wave propagation.