MEDIUM
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IMPORTANT
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The least value of |z-3-4i|2+|z+2-7i|2+|z-5+2i|2occurs when z=x+iy then the real part of z is

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Important Questions on Complex Numbers

MEDIUM
JEE Main/Advance
IMPORTANT
Find the modulus, argument and the principal argument of the complex numbers.
(a) z=1+cos10π9+isin10π9
MEDIUM
JEE Main/Advance
IMPORTANT
Find the modulus, argument and the principal argument of the complex numbers.
(b) (tan1-i)2
MEDIUM
JEE Main/Advance
IMPORTANT

Find the modulus, argument and the principal argument of the complex number z=5+12i+5-12i5+12i-5-12i

MEDIUM
JEE Main/Advance
IMPORTANT
Given that x,yR, solve :4x2+3xy+2xy-3x2i=4y2-x22+3xy-2y2i
MEDIUM
JEE Main/Advance
IMPORTANT
If iz3+z2-z+i=0, then prove that |z|=1.
HARD
JEE Main/Advance
IMPORTANT
For complex numbers z&ω, prove that, |z|2ω-|ω|2z=z-ω if and only if, z=ω or zω¯=1
HARD
JEE Main/Advance
IMPORTANT

Let z1,z2 be complex numbers with z1=z2=1, prove that z1-1+z2+1+z1z2+14

MEDIUM
JEE Main/Advance
IMPORTANT
Interpret the following locii in zC.
(a) 1<|z-2i|<3