You input a complex number, and it will output the real Someone write the real part, give me the real part of z. Used to the notation, sometimes you'll see Use for complex numbers- let's say that z isīecause it has a real part and it has an imaginary part. Let's call it z- and z is the variable we do tend to
So you're probablyįamiliar with the idea. Ways to represent and visualize complex numbers. In this video is make sure we're comfortable with It would be good to watch as many of the advanced math videos on Khan Academy as you can to be able to encounter some of these alternate forms. If you want to skip algebra and trigonometry you may run into several examples of this- where your textbook has simplified things that you will have to get used to in their more conventional form. If two angles are given, theta is the first by convention and phi is second fiddle. I am guessing you are not asking about that-phi is often used for the arguments in physics and in Argand diagrams, but theta is also used. One other thing that is different in your question is the phi and the theta.
Natural logs are to the base e for example. It offers a format that is a lot more promising for getting to a solution because you can use a lot more tools to manipulate it. It is used to find roots of functions, and is a shorthand way of expressing a complex number, for example in calculus. It is the exponential form of the same relationship. Once you get into logarithms, the concept of re^i(phi) becomes a lot easier and it becomes second nature to convert back and forth. Usually re^i(phi) form is taught in calculus or perhaps introduced in precalc, with more about logarithms and transcendentals. I'm not so fond of the cis notation because it obscures the really cool things about how sin and cos and theta can be related as complex numbers, but that is just my preference-I love to see how things tick. So, r cis theta just means r times cis theta and is therefore the same as rcos theta+risin theta or r(cos theta + i sin theta)
You can double check to make sure that adding or subtracting 180° (or doing nothing) gives you an answer in the same quadrant as the original point.Ĭis theta is just shorthand for cos theta + i sin theta If not, just add or subtract 180° to get it into the correct quadrant.
Now, check to see if your result is in the same quadrant as the original point a + bi. or Re-axis) and traveling counter-clockwise to +180°. Remember that instead of a circle that goes from 0° to 360°, we are starting at -180° (the negative x-axis. Next, work the problem and get the result.įinally, think about which quadrant your final answer should be in - this will be the same quadrant that the original point lies in. You can do this by thinking about the signs of a (the real part) and b (the imaginary part): First, figure out which quadrant the point a + bi lies in.
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