I am new to quantum computing and reading the book "Introduction to Classical and Quantum Computing", by Wong (link).
I do not understand how to calculate the qubit state for the below question. Can someone please help me understand the answer? Thanks
Excercis 2.11. The following two states are opposing points on the Bloch sphere: $$|a\rangle=\frac{\sqrt 3}{2}|0\rangle+\frac{i}{2}|1\rangle,$$ $$|b\rangle=\frac{i}{2}|0\rangle+\frac{\sqrt 3}{2}|1\rangle.$$ So, we can measure relative to them. Now consider a qubit in the state $$\frac{1}{2}|0\rangle-\frac{\sqrt 3}{2}|1\rangle.$$
(a) Write the qubit's state in terms of $|a\rangle$ and $|b\rangle$.
(b) If you measure the qubit in the basis $\{|a\rangle,|b\rangle\}$, what states would you get and with what probabilities?