Find the exact value of given that and . (Both u and v are in Quadrant II.)

Question

Find the exact value of  given that  and  . (Both u and v are in Quadrant II.)

Quizplus · Accepted Answer

In order to find the value of 11eb80b1_afbb_f6cc_a291_cfbcaceff47a_TB8633_11, we need to find the complex number z such that z^2 = 11eb80b1_afbc_1ddd_a291_41bbb74dfed1_TB8633_11 and Im(z) > 0 (since it's in Quadrant II).

Let's start by finding the square root of 11eb80b1_afbc_1ddd_a291_41bbb74dfed1_TB8633_11:
sqrt(11eb80b1_afbc_1ddd_a291_41bbb74dfed1_TB8633_11) = 37c4e70d_4f8e_836a_6e60_2f16e6bdf3af_TB8633_11

Now we need to add the imaginary part of this square root to get the desired complex number:
z = sqrt(11eb80b1_afbc_1ddd_a291_41bbb74dfed1_TB8633_11) + 11eb80b1_afbc_1dde_a291_557ea3d7dea6_TB8633_11
  = 37c4e70d_4f8e_836a_6e60_2f16e6bdf3af_TB8633_11 + 11eb80b1_afbc_1dde_a291_557ea3d7dea6_TB8633_11
  = 11eb80b1_afbc_44f1_a291_e3e699ace4a6_TB8633_11

Therefore, the value of 11eb80b1_afbb_f6cc_a291_cfbcaceff47a_TB8633_11 is 11eb80b1_afbc_44f1_a291_e3e699ace4a6_TB8633_11. The correct answer is C.

Find the Exact Value of Given That and