The equation 2i 6 7i is a complex number equation, which can be difficult to interpret and solve at first glance. Complex numbers are usually written in the form of a+bi, where a is the real part and b is the imaginary part. In this equation, 2i is the real, and 6 7i is the imaginary part. To find the equivalent of this equation, we must first understand how to manipulate complex numbers.
Understanding Complex Numbers
Complex numbers can be represented in two ways, rectangular and polar. In rectangular form, a complex number is written as a+bi, where a is the real part and b is the imaginary part. In polar form, a complex number is written in terms of its magnitude, or modulus, and argument, or angle. The modulus is the distance from the origin to the complex number, and the argument is the angle formed from the real axis to the complex number.
Manipulating Complex Numbers
Since complex numbers can be manipulated and operated on in the same way as real numbers, such as addition, subtraction, multiplication, and division, they can be used to solve equations and functions. To find the equivalent of 2i 6 7i, we can use the properties of complex numbers and basic algebra to manipulate the equation.
Solving for 2i 6 7i
To solve for the equivalent of 2i 6 7i, we must first multiply the equation by its conjugate, which is 2i – 7i. The conjugate of a complex number is the number with the same real part and opposite imaginary part. By multiplying the equation by its conjugate, the real part of the equation is eliminated and only the imaginary part remains. We can then divide both sides of the equation by the magnitude of the conjugate, which is the square root of 4 + 49, or 7.
Conclusion
The equivalent of 2i 6 7i is the imaginary part of the equation, 6 7i, divided by the magnitude of its conjugate, which is 7. Therefore, the equivalent of 2i 6 7i is 6 7i/7, or 6i.
