The free JEE Advanced Maths diagnostic

8 questions, about 5 minutes. We name the exact JEE Advanced misconception losing you marks -- not “you need more practice”, the specific pattern -- and point you at the targeted lesson that fixes it.

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JEE Advanced Maths Diagnostic: Complex NumbersQuestion 1 of 8

The equation $z^{2} + 16 = 0$ has the two roots $z = 4i$ and $z = -4i$ .

What is $|4i|^{2} + |-4i|^{2}$ (the sum of the squared moduli of the two roots)?

32

, since each squared modulus is

4^{2} = 16

, so

16 + 16 = 32

-32

, squaring the roots directly:

(4i)^{2} + (-4i)^{2} = -16 - 16

0

, because the two roots are opposites, so their squares cancel

16

, because both roots give the same squared modulus, so count it once

The free JEE Advanced Maths diagnostic