1
GATE IN 1997
MCQ (Single Correct Answer)
+1
-0.3
The complex number $$z\, = \,x\, + \,jy$$ which satisfy the equation $$\left| {z + 1} \right|\, = \,1$$ lie on
A
a circle with ( 1, 0 ) as the center and radius 1
B
a circle with ( - 1, 0 ) as the center and radius 1
C
y-axis
D
x-axis
2
GATE IN 1994
MCQ (Single Correct Answer)
+1
-0.3
The real part of the complex number $$z\, = \,x\, + \,iy$$ is given by
A
$${\mathop{\rm Re}\nolimits} (z)\, = \,z\, - \,{z^*}$$
B
$${\mathop{\rm Re}\nolimits} (z)\, = \,{{z\, - \,{z^*}} \over 2}$$
C
$${\mathop{\rm Re}\nolimits} (z)\, = \,{{z\, + \,{z^*}} \over 2}$$
D
$${\mathop{\rm Re}\nolimits} (z)\, = \,z\, + \,{z^*}$$
3
GATE IN 1994
MCQ (Single Correct Answer)
+1
-0.3
$$\cos \phi $$ can be represented as
A
$${{{e^{i\phi }}\, - \,{e^{ - i\phi }}} \over 2}$$
B
$${{{e^{i\phi }}\, - \,{e^{ - i\phi }}} \over {2i}}$$
C
$${{{e^{i\phi }}\, + \,{e^{ - i\phi }}} \over i}$$
D
$${{{e^{i\phi }}\, + \,{e^{ - i\phi }}} \over 2}$$
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