Solveeit Logo
Login

Question

Question: \(\frac{(1 + i)^{2}}{(2 - i)}\) form of \(\frac{1}{5}\) is....

(1+i)2(2−i)\frac{(1 + i)^{2}}{(2 - i)} form of 15\frac{1}{5} is.

A

35\frac{3}{5}

B

45\frac{4}{5}

C

z≠0z \neq 0

D

None of these

Answer

35\frac{3}{5}

Explanation

Solution

L.H.S. a2+b2+c2+2a+a2−b2−c2+2ib(1+a)1+1+2ac+2(a+c)=2a(a+1)+2ib(1+a)2(1+a)(1+c)=a+ib1+c\frac{a^{2} + b^{2} + c^{2} + 2a + a^{2} - b^{2} - c^{2} + 2ib(1 + a)}{1 + 1 + 2ac + 2(a + c)} = \frac{2a(a + 1) + 2ib(1 + a)}{2(1 + a)(1 + c)} = \frac{a + ib}{1 + c}

z1=a+ib,z2=c+idz_{1} = a + ib,z_{2} = c + id