The quadratic formula works whether the coefficients of the equation are real or complex. solve the following equations using the quadratic formula and, if necessary, de moivre's theorem. (enter your answers as a comma-separated list.)

z2 − 2iz − 5 = 0

z=i+2

,

z=i-2

Step-by-step explanation:

Remember that the quadratic equation has the complex solutions (this is the quadratic formula).

Apply this with a=1, b=-2i and c=-5 to get:

. Then the solutions are

and

It isn't necessary to use De Moivre's formula.  

b. 6

step-by-step explanation:

we are given the table representing an exponential function.

we can see from the table that, as x is increasing, the value of y is increasing in the power of 6.

i.e. the following relation is obtained,

x = 1, y = 6

x = 2, y = 36 =

x = 3, y = 216 =

x = 4, y = 1296 =

x = 5, y = 7776 =

so, the geometric series obtained is .

thus, the common ratio is given by = = 6.

hence, the common ratio is 6.

step-by-step explanation: