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Algebra   involves Imaginary numbers. The imaginary number can be added with real number to form complex numbers. The results of quadratic equation involve imaginary numbers. When imaginary numbers are squared, they give a negative result. The imaginary number (like 1 for Real Numbers) is i, which is the square root of 1.

Square root of -1 = i.  An imaginary number can be written as a real number multiplied with imaginary unit. Rules of radical are used in finding powers of i. Imaginary numbers are used in areas such as signal processing, control theory, electro magnetism, etc.

Two complex numbers (a + ib) and (c + id) are said to be equal if and only if a=c and b=d.

Let us have some example problems for imaginary numbers as well as other problem. This is shown as below:-

Example 1:- Simplify square root of -18

Solution 1:-

For the given equation √-18, we can use the rule for simplifying the square root for rewrite imaginary numbers

We know that, square root of -18 = square root of 9 times square root of 2 = 3 square root of 2 (by neglecting negative sign)

So 3i square root of 2 is the most simplified form of square root of -18

Example 2:-

Simplify (5i + 2i)

Solution 2:-

For the given equation, we need to take i common from both sides

Therefore,

(5i + 2i) =(5 + 2) i   (by combining like terms)

= 7 i

Therefore 7i is the simplified form of (5i + 2i)