Complex Numbers and Complex Functions
... Definition 1.5. We define the polar exponential function to be eiϑ = cos (ϑ) + i sin (ϑ). Note that eiϑ is a function of a real variable ϑ and the values of the function are evaluated by simply putting in the values of ϑ. The polar exponential function satisfies a number of properties shared with th ...
... Definition 1.5. We define the polar exponential function to be eiϑ = cos (ϑ) + i sin (ϑ). Note that eiϑ is a function of a real variable ϑ and the values of the function are evaluated by simply putting in the values of ϑ. The polar exponential function satisfies a number of properties shared with th ...
The Complex Number System The need for extending the real
... The need for extending the real number system is evident when considering solutions of simple equations. For example, the equation x2 + 1 = 0 has no real number solutions, for if x is any real number, then x2 ≥ 0 and so x2 + 1 ≥ 1. We extend the real number system to the system of complex numbers in ...
... The need for extending the real number system is evident when considering solutions of simple equations. For example, the equation x2 + 1 = 0 has no real number solutions, for if x is any real number, then x2 ≥ 0 and so x2 + 1 ≥ 1. We extend the real number system to the system of complex numbers in ...
Note on exponential and log functions.
... for rational numbers m/n. One observes that this function, so far defined only for rational numbers, has the usual properties of an exponential. (2) One shows that ax is a continuous function of the rational variable x. Now one has to show that this function can be extended to a continuous function ...
... for rational numbers m/n. One observes that this function, so far defined only for rational numbers, has the usual properties of an exponential. (2) One shows that ax is a continuous function of the rational variable x. Now one has to show that this function can be extended to a continuous function ...
Grade 7 Maths Term 1
... The square root sign works like a bracket. Simplify any addition or subtraction underneath the sign where possible. Example ...
... The square root sign works like a bracket. Simplify any addition or subtraction underneath the sign where possible. Example ...
Powers and Roots Student Notes
... Where n is a natural number, and a and b are real numbers. Refer to the Perfect Square/Cube chart. In the chart, fill in all perfect squares from 1 -22 and all perfect cubes from 1-10. This chart will be instrumental in helping us simplifying radicals. We can use this property to simplify square roo ...
... Where n is a natural number, and a and b are real numbers. Refer to the Perfect Square/Cube chart. In the chart, fill in all perfect squares from 1 -22 and all perfect cubes from 1-10. This chart will be instrumental in helping us simplifying radicals. We can use this property to simplify square roo ...
