JEE Main Mathematics: Complex Numbers Practice Questions

15 questions with answers and step-by-step solutions. Tap any question to see the full worked solution.

Q1.
$Find the modulus of the complex number 3 + 4i.$
Easy
Q2.
$Simplify the expression (1 + i) + (2 - 3i).$
Easy
Q3.
$What is the conjugate of the complex number 2 - 5i?$
Easy
Q4.
$What is the real part of the complex number 7 - 9i?$
Easy
Q5.
$What is the value of i raised to the power of 402?$
Easy
Q6.
$If z is a complex number such that |z - 3| + |z + 3| = 8, then the maximum value of |z| is$
Medium
Q7.
$If z = x + iy satisfies |z + 1| = |z - 1|, then the locus of z is$
Medium
Q8.
$The amplitude of the complex number (1 + i sqrt(3)) / (sqrt(3) + i) is$
Medium
Q9.
$I f o m e g ai s a co m pl e x c u b er oo t o f u ni t y, t h e n t h e v a l u eo f (1 + o m e g a - o m e g a s q u a r e d)^{7} i s$
Medium
Q10.
$I f t h eco m pl e x n u mb er sz 1, z 2, an d z 3 r e p r ese n tt h e v er t i ceso f an e q u i l a t er a l t r ian g l e, t h e n z 1^{2} + z 2^{2} + z 3^{2} e q u a l s$
Medium
Q11.
$If z is a complex number such that |z - 3 - 2i| = 2, then the maximum value of |2z - 6 + 5i| is$
Hard
Q12.
$I f o m e g ai s a co m pl e x c u b er oo t o f u ni t y, t h e n t h e v a l u eo f t h es u m f r o mk = 1 t o 100 o f (o m e g a^{k} + o m e g a^{(} k + 1)) i s$
Hard
Q13.
$If z1 and z2 are two complex numbers such that |z1 + z2| = |z1| + |z2|, then arg(z1) - arg(z2) is$
Hard
Q14.
$L e t z b e a co m pl e x n u mb er s a t i s f y in g ∣ z^{2} - 1∣ = ∣ z ∣^{2} + 1. T h e n z l i eso n$
Hard
Q15.
$T h e n u mb er o f co m pl e x n u mb er sz s u c h t ha t ∣ z ∣ = 1 an d ∣ z^{4} + z^{3} + z^{2} + z + 1∣ = 0 i s$
Hard

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