Question

Express the following in the form of a+ib,a,b€R,i=√-1 State the value of a and b,z=2+i|(3-i)(1+2i)​

Answer 1

Answer:

$z = \frac{2 + i}{(3 - i)(1 + 2i)} = \frac{3}{10} - i \frac{1}{10}$

Step-by-step explanation:

To express the following in the form of a+ib,a,b€R,i=√-1 and also to state the value of a and b,

z=2+i|(3-i)(1+2i)

$z = \frac{2 + i}{(3 - i)(1 + 2i)} \\ \\ z = \frac{2 + i}{3 + 6i - i - 2 {i}^{2} } \\ \\ z = \frac{2 + i}{3 + 6i - i - 2( - 1) } \\ \\ z = \frac{2 + i}{5 + 5i} \\ \\ z = \frac{1}{5} \Big(\frac{2 + i}{1 + i} \Big) \times \Big( \frac{1 - i}{1 - i} \Big) \\ \\ z= \frac{1}{5} \Big(\frac{(2 + i)(1 - i)}{ {1}^{2} - {(i)}^{2} } \Big) \\ \\ z = \frac{1}{5} \Big(\frac{2 - 2i + i - {i}^{2} }{2}\Big) \\ \\ z = \frac{1}{10} (3 - i) \\ \\ z = \frac{3}{10} - i \frac{1}{10}$

so,the value of a and b are 3/10 and -1/10

Hope it helps you.