No, you did not have that before- you are getting ahead of yourself!nirvana1990 said:Ooh thanks that was quite helpful but now i seem to have over-simplified somehow!
I got: cos^2x-sin^2x+2isin2xcos2x
Since you do have 2 sin x cos x, it should be obvious exactly where to use that!=cos2x+2isin2xcos2x (by using cos^2x-sin^2x=cos2x)
Then would you divide by cos2x to give: 1+2isin2x? Or should I use sin2x=2sinxcosx somewhere??
A complex number is a number that has both a real and an imaginary component. It is typically expressed in the form a + bi, where a is the real part and bi is the imaginary part, represented by the imaginary unit i (where i = √-1).
A real number is any number that can be plotted on a number line, including positive and negative numbers, fractions, and decimals. An imaginary number, on the other hand, is any number that involves the square root of a negative number, such as √-4. It cannot be plotted on a number line and is typically represented by the letter i.
To add or subtract two complex numbers, simply combine the real parts and the imaginary parts separately. For multiplication, use the FOIL method as you would for binomials. To divide two complex numbers, multiply the numerator and denominator by the complex conjugate of the denominator, which is the same number with the sign of the imaginary part flipped.
Yes, complex numbers can be graphed on a coordinate plane, with the real part representing the x-axis and the imaginary part representing the y-axis. The point where the two axes intersect represents the origin, or 0 + 0i.
Complex numbers are used in a variety of fields, including engineering, physics, and signal processing. They are also used in the study of electric circuits, fluid dynamics, and quantum mechanics. In everyday life, complex numbers can be used to describe the motion of objects, analyze financial data, and even create realistic computer-generated images in movies and video games.