JEE Advanced Mathematics: Complex Numbers Practice Questions

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

Q1.
$Find the value of i raised to the power of 4n plus 3, where n is a positive integer.$
Easy
Q2.
$If z is a complex number such that z plus conjugate of z equals 0, then z must be purely imaginary.$
Easy
Q3.
$What is the argument of the complex number 1 plus i?$
Easy
Q4.
$What is the modulus of the complex number 3 plus 4i?$
Easy
Q5.
$What is the multiplicative inverse of the complex number i?$
Easy
Q6.
$If the amplitude of (z - 1) / (z + 1) is pi/4, then the locus of z is$
Medium
Q7.
$I f z 1 an d z 2 a r e tw oco m pl e x n u mb er ss u c h t ha t ∣ z 1∣ = 1 an d ∣ z 2∣ = 1, t h e n t h e v a l u eo f ∣ z 1 + z 2 ∣^{2} + ∣ z 1 - z 2 ∣^{2} i s$
Medium
Q8.
$If omega is a complex cube root of unity, then the value of the product of (1 - omega + omega squared) multiplied by (1 + omega - omega squared) is equal to whi$
Hard
Q9.
$Let z be a complex number satisfying |z| = 1. If the argument of z is theta, then the argument of (1 + z) / (1 - z) is equal to which of the following?$
Hard

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Complex Numbers — JEE Advanced Mathematics Practice Questions with Solutions | SolveGini