
MathWithout loss of generality assume that ` ``z = r + 0i` . Since we have that `w = (e^(2pi i))^(1/3)` ( using `e^(2pi i) = 1 + 0i = 1` ) then `w = e^((2pi)/3i)` In cartesian coordinates, `w =...

MathQ. Triangle ABC, A`(z_1)` ,B`(z_2)` ,C`(z_3)` is inscribed in the circle `z=2` .If the internal...Call the angle CAD `theta` . Since AD bisects the angle at A (CAB), then angle DAB is equal to CAD, ie `theta` . Using the circle theorems, CAD is equal to CBD, since they are subtended from the...

MathWe want the value of the expression `ilog(xi) + i^2pi + i^3log(x+i) + i^4(2tan^(1)x)` given that `x>0`. Firstly consider the complex inverse tangent function `tan^(1)z = i/2[log(1iz)...

MathWe have the complex number `z = 8(cos((4pi)/5) + isin((4pi)/5))` First convert z into polar coordinates (argument,modulus) on the complex plane. ` `We can see that the argument of z, `arg(z) =...

MathWe have `z = (5sqrt(3))/2 + (5/2)i`, `w = 1 + sqrt(3)i` a) the polar form of a complex number consists of the argument and the modulus. Now, `arg(z) = pi/2 + tan^(1)(((5sqrt(3))/2)/(5/2)) =...