A) \[2-\frac{3}{2}i\]
B) \[\frac{3}{2}+2i\]
C) \[\frac{3}{2}-2i\]
D) \[-2+\frac{3}{2}i\]
Correct Answer: C
Solution :
\[|z|-z=1+2i\] Let \[z=x+iy\], therefore \[|x+iy|-(x+iy)=1+2i\] Equating real and imaginary parts, we get \[\sqrt{{{x}^{2}}+{{y}^{2}}}-x=1\]and \[y=-2\]Þ\[x=\frac{3}{2}\] Hence complex number\[z=\frac{3}{2}-2i\]. Trick: Since \[\left| \frac{3}{2}-2i \right|-\left( \frac{3}{2}-2i \right)\] \[=\sqrt{\frac{9}{4}+4}-\frac{3}{2}+2i=\frac{5}{2}-\frac{3}{2}+2i=1+2i\]
You need to login to perform this action.
You will be redirected in
3 sec
