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The square root of minus one √ (−1) is the "unit" Imaginary Number, the equivalent of 1 for Real Numbers. In mathematics the symbol for √ (−1) is i for imaginary. But in electronics the symbol is j, because i is used for current, and j is next in the alphabet.
To multiply two complex numbers z1 = a + bi and z2 = c + di, use the formula: z1 * z2 = (ac - bd) + (ad + bc)i. A complex number is a number that can be expressed in the form a + bi, where a and b are real numbers and i is the imaginary unit, which is defined as the square root of -1.
Definition. The imaginary unit i is defined solely by the property that its square is −1: With i defined this way, it follows directly from algebra that i and −i are both square roots of −1.
One way is to convert the complex number into polar form. For $z = re^{i\theta}$, $z^2 = r^2 e^{i(2\theta)}$. So to take the square root, you'll find $z^{1/2} = \pm \sqrt{r} e^{i\theta/2}$. Added: Just as with the nonnegative real numbers, there are two complex numbers whose square will be $z$. So there are two square roots (except when $z = 0$).
-1 is 1 rotated over $\pi$ radians. The square root of a number on the unit circle is the number rotated over half the angle, so $i$, or $\sqrt{-1}$ is 1 rotated over $\pi/2$ radians. To find $\sqrt{i}$ you just half the angle again: $\pi/4$ radians. The corresponding real and imaginary parts are $\cos\frac{\pi}{4}$ and $\sin\frac{\pi}{4}$ resp ...
An imaginary number is a complex number that can be written as a real number multiplied by the imaginary unit $i$, which is defined by its property $i^2 = −1$. There is no problem in understanding that why $-1$ is a real number as you can easily construct a line and represent $-1$ on that line.
The imaginary numbers are numbers that result in negative numbers when raised to even powers. An imaginary number is the product of a non-zero real number and iota i where i is square root of -1.
The imaginary number i is defined as the square root of -1, and we can use it in algebraic expressions. An imaginary number (in general) is defined as a number that can be written as a product of a real number and i. For instance, 4i and -15i are imaginary numbers.
The imaginary number i=sqrt(-1), i.e., the square root of -1. The imaginary unit is denoted and commonly referred to as "i."
i (unit imaginary number) more ... The square root of minus 1. The symbol is i. It is a number that, when multiplied by itself, produces −1. But when we square any Real Number we always get a positive, or zero, result. Examples: 2 × 2 = 4, and. (−2) × (−2) = 4 also.