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

We need to find out the value of $11eacce6_1e99_9f4e_9f49_e3579a80b007_TB7896_11$. 
Since $u$ is in Quadrant II, we know that its real part is negative and its imaginary part is positive. Therefore, we can eliminate choices A and D, which have a positive real part.
Next, we can look at the values of $v$ in the given numbers. We see that the difference between the values of $v$ in the two given numbers is $0xc1d4e3ccc3$. Therefore, subtracting this difference from the value of $v$ in the second given number should give us the value of $v$ in the number we are looking for. 
\begin{align*}
(0x1d744f32e6b0 - 0xc1d4e3ccc3) &= 0x11b2fb6592ed \
\Rightarrow 11eacce6_1e9a_b0c0_9f49_1d744f32e6b0_TB7896_11 - 0x11b2fb6592ed &= 11eacce6_1e9b_4d03_9f49_d7281965511f_TB7896_11 
\end{align*}
Therefore, the answer is choice C.

Find the Exact Value of Given That and