True or False
State True or False for the following:
If z is a complex number such that z ≠ 0 and Re(z) = 0, then Im(z2) = 0.
This statement is False.
Let z = x + yi, z ≠ 0 and Re(z) = 0
Since real part is 0.
⇒ x = 0
∴ z = 0 + yi = yi
∴ lm(z2) = y2i2
= –y2 which is real.
Concept: The Modulus and the Conjugate of a Complex Number
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