Question

express in the form of a+ib also find modulus
(i) 3+i/2-i​

Answer 1

$let \: \: \: \: z = \frac{3 + i}{2 - i} \\ z = \frac{3 + i}{2 - i} \times \frac{2 + i}{2 + i} \\ z = \frac{6 + 3i + 2i + {i}^{2} }{ {2}^{2} - {i}^{2} } \\ z = \frac{6 - 1 + 5i}{4 - ( - 1)} \\ z = \frac{5 + 5i}{5} \\ z = 1 + i \\ \\ |z| = \sqrt{ {1}^{2} + {1}^{2} } \\ |z| = \sqrt{2}$