Solve by taking square roots:
A) 10
B) -10
C) -10i, 10i
D) -10, 10
E) 0, 10

Question

Solve by taking square roots: 
A) 10 
B) -10 
C) -10i, 10i 
D) -10, 10 
E) 0, 10

Quizplus · Accepted Answer

Taking the square root of a complex number involves finding the square root of its magnitude and dividing the argument by 2. The magnitude of the given complex number is:

|11eb69da_9f30_e284_af94_4f50427ad5a3_TB8311_11| = sqrt(11eb69da_9f30_e284_af94_4f50427ad5a3^2 + TB8311_11^2) = sqrt(2285)

The argument of the given complex number is:

arg(11eb69da_9f30_e284_af94_4f50427ad5a3_TB8311_11) = arctan(TB8311_11 / 11eb69da_9f30_e284_af94_4f50427ad5a3)

So, the two square roots are:

sqrt(2285) * exp(i*arctan(TB8311_11 / 11eb69da_9f30_e284_af94_4f50427ad5a3) / 2) and sqrt(2285) * exp(i*arctan(TB8311_11 / 11eb69da_9f30_e284_af94_4f50427ad5a3 + pi) / 2)

Since the magnitude is positive, both square roots are real numbers. Therefore, the best choice is D) -10, 10.

Solve by Taking Square Roots