Complex Numbers and De Moivre’s Theorem — Important Questions

3

For a complex number \( a + bi \), the imaginary part is \( b \), not \( bi \). So here, it is 3.

1

We know \( i^2 = -1 \), so \( i^4 = (i^2)^2 = (-1)^2 = 1 \).

3 - 4i

The conjugate of \( a + bi \) is \( a - bi \). So, the conjugate of \( 3 + 4i \) is \( 3 - 4i \).

True

Yes, because a real number is \( a + 0i \), and its conjugate is \( a - 0i = a \), which is the same.