GATE IN 1994 | Complex Variable Question 11 | Engineering Mathematics

GATE IN 1994

MCQ (Single Correct Answer)

-0.3

The real part of the complex number $$z\, = \,x\, + \,iy$$ is given by

$${\mathop{\rm Re}\nolimits} (z)\, = \,z\, - \,{z^*}$$

$${\mathop{\rm Re}\nolimits} (z)\, = \,{{z\, - \,{z^*}} \over 2}$$

$${\mathop{\rm Re}\nolimits} (z)\, = \,{{z\, + \,{z^*}} \over 2}$$

$${\mathop{\rm Re}\nolimits} (z)\, = \,z\, + \,{z^*}$$

GATE IN 1994

MCQ (Single Correct Answer)

-0.3

$$\cos \phi $$ can be represented as

$${{{e^{i\phi }}\, - \,{e^{ - i\phi }}} \over 2}$$

$${{{e^{i\phi }}\, - \,{e^{ - i\phi }}} \over {2i}}$$

$${{{e^{i\phi }}\, + \,{e^{ - i\phi }}} \over i}$$

$${{{e^{i\phi }}\, + \,{e^{ - i\phi }}} \over 2}$$

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Engineering Mathematics