Solveeit Logo
Login

Question

Question: The imaginary part of \(\frac{1}{2} + \frac{9}{2}i\)is....

The imaginary part of 12+92i\frac{1}{2} + \frac{9}{2}iis.

A

12−92i\frac{1}{2} - \frac{9}{2}i

B

14−94i\frac{1}{4} - \frac{9}{4}i

C

14+94i\frac{1}{4} + \frac{9}{4}i

D

None of these

Answer

14+94i\frac{1}{4} + \frac{9}{4}i

Explanation

Solution

We have (1+i)22−i=(2i)(2+i)(2−i)(2+i)\frac { ( 1 + i ) ^ { 2 } } { 2 - i } = \frac { ( 2 i ) ( 2 + i ) } { ( 2 - i ) ( 2 + i ) }

a=0,b=1a = 0,b = 1.

Thus Im 1+b+ia1+b−ia=1+1+01+1−0=1\frac{1 + b + ia}{1 + b - ia} = \frac{1 + 1 + 0}{1 + 1 - 0} = 1.