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A Journey into the World of Complex Numbers-Class 11
COMBINATIONS AND HOW TO USE IT-VALUE FOR MONEY
You probably find Complex numbers easy! Having taught Mathematics for three decades to high school students and college students, I can conclude that what you learn in High School, in Complex numbers is fairly easy. However, if you take Mathematics in College, you're going to use quite a lot of Complex numbers.
This is where this comes in handy! To start with you need to remember that a complex number has a real part, denoted by Rez and an imaginary part denoted by Imz. You'll learn how to perform elementary operations on Complex numbers such as addition, subtraction, multiplication and division.
You need to remember powers of i upto the 4th power. Interestingly, you'll note that powers of i are in a cyclic form up to the 4th powers. Next, you'll learn how to find the modulus and conjugate of a complex number.
In this context, a lot of problems need to be practiced. You have formulas for calculating the modulus of a product and quotient. Likewise, you can also calculate the conjugate of a sum, difference, product and quotient.
Moving on, you'll learn about the polar form of a complex number, where you'll learn to calculate the modulus and amplitude of the complex number. The amplitude is also called the argument. There's an interesting method of calculating the amplitude which is illustrated in the videos below.
Locus of a complex number is what you need to be looking at next. A simple way to do this is to just write z=x+iy and simplify it given the equation. The next topic you'll learn is how to calculate the square root of a complex number.
This is a fairly easy concept to master. While writing the square roots, keep in mind that if the product is positive, both x and y have to be either positive or negative. While, if the product is negative, one of x , y is positive and the other is negative.
You'll conclude with learning cube roots of unity and properties based on these. This is one of the easiest topics you'll learn in complex numbers, but incredibly important as well as it's used in other branches of Math.
So, that concludes Complex numbers. You can sign up for online tutoring if you need extra help.
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