Draw each of the following complex numbers on an Argand diagram, and find their modulus and argument.
a) (1/2, -1/sqrt12)
b) -2i
c) -sqrt3 + sqrt(3i)
I think I know how to draw the complex numbers on the diagram, but what does it mean by modulus and argument? Can someone explain the steps to me please?
Doesn't your text book, if it has problems asking for "modulus" and "argument", have definitions of those terms?
Writing a complex number in the form "x+ iy" is "Cartesian form" since it is using the x and y values of a Cartesian coordinate system on the Argand plane. "Polar form" is of the form " " or (more advanced) " " where r is the straight line distance from (0,0) (the number 0) to (x, y) (the number x+iy) and is that angle the line from the origin to the number makes with the number- in other worlds "polar coordinates".
In any case, the "modulus" of a complex number, also called its "absolute value", is the distance, r, and the "argument" is the angle . If, from the point (x, y) (representing x+ iy), you drew the line from (0, 0) to (x, y), the line from (x,y) to (x, 0), and the line from (0, 0) to (x, 0), you get a right triangle with sides of length x, y, and r, and angle at the origin [itex]\theta[/itex]. From the Pythagorean theorem, so that . From the definition of the "tangent" function, so that (as long as x is not 0 in which case the argument is infinite). I'll bet your text book has those formulas.