Question

find the general value of √-i​

Answer 1

Answer:

To find this you need Euler’s Formula:

eiθ=cos(θ)+isin(θ)

To make the right side equal to −i , you need cos(θ)=0 and sin(θ)=−1 . The closest solution to 0 is θ=−π2 , and the real solutions will repeat every 2π in either direction. So the powers of e you need are i(−π2+2πn) .

Answer 2

Step-by-step explanation:

The value of i is √-1. The imaginary unit number is used to express the complex numbers, where i is defined as imaginary or unit imaginary. We will explain here imaginary numbers rules and chart, which are used in Mathematical calculations. The basic arithmetic operations on complex numbers can be done by calculators. The imaginary number i is also expressed as j sometimes. Basically the value of imaginary i is generated, when there is a negative number inside the square root, such that the square of an imaginary number is equal to the root of -1. But when we take the cube of i, the value is -i. It is a solution to the quadratic equation or expression, x2+1 = 0, such as;

x2 = 0 – 1

x2 = -1

x = √-1

x = i

Therefore, an imaginary number is the part of complex number which we can write like a real number multiplied by the imaginary unit i, where i2 = -1. The imaginary number, when multiplied by itself, gives a negative value. For example, consider an imaginary number 3i, if multiplied by itself or if we take the square of 3i, gives 9i2 or we can write it as -9. Also, 0 is considered as both the real number and an imaginary number.

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