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Question

The complex number -3+3ii-13+3ii3+3iwhen represented in Argand diagram lies in which of the following.


A

In the first quadrant

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B

In the second quadrant

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C

On the Y-axis (imaginary axis)

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D

On the X- axis (real axis)

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Solution

The correct option is C

On the Y-axis (imaginary axis)


Explanation of correct answer :

Determining where complex number z lies by simplifying the expression:

Given, z=-3+3ii-13+3ii3+3i

Taking 3 outside,

z=3-1+3ii-1323+ii1+i=13-1+3i(i-1)-1+3i(i+1)=13(i-1)(i+1)

Rationalize z, by multiplying its numerator and denominator by (i-1).

z=13(i-1)(i+1)(i-1)(i-1)=13i2+1-2ii2-1=-13i(i2=-1)

Hence, z lies on Y-axis because it is purely imaginary.

Thus, the correct answer is Option (C).


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