The set of complex numbers is the set of all numbers of the form a + bi, where a and b are real numbers and i = . a. true b. false

The set of complex numbers IS the set of all numbers of the form , where a and b are real numbers, and i is the imaginary unit defined as , therefor the statement is correct.

Complex numbers can be seen as an extension of the set of all real numbers, and they have a wide range of aplications in many fields like Engineering, Physics, Mathematics and more. The most simple definition of a complex number, is that they are the sum of a real number (in this case a) and an imaginary number (in this case ).

Usually confusion arises in many students while studying complex numbers because the imaginary unit, i, isn't a number we can compute. The best way to see these numbers is as 2-dimensional numbers, meaning numbers that have 2 components (the idea is almost the same as that of a 2-dimensional vector). They are thoroughly used in Mechanical Engineer to solve for vibration problems, and in Electrical Engineering to compute the real and imaginary part of electric power.

Complex numbers, imaginary unit, real numbers

step-by-step explanation:

this can be solved first with pythagorean theorem, which tells us to square both legs of the triangle and sum it. this will be equal to the square of the hypotenuse.

the hypotenuse is the side "opposite" the 90 degree angle, which is x.

so we can write using pythagorean theorem,

simplifying:

to further simplify this radical, we need to use the property  

thus