Let z1 = x + iy and z2 = a + ib:Suppose z1 = z2: Which of the following is/are true?
A. x2

Question

Let z1 = x + iy and z2 = a + ib:Suppose z1 = z2: Which of the following is/are true?
A. x2

anonymous · Answer

$$z_1=x+iy,~z_2=a+ib$$
If $z_1=z_2$, then $x=a$ and $y=b$. The first can't always be true. Consider $z_1=z_2=1$. Then $x^2a^2=x^4=1^4=1$, but $b^2y^2=y^4=0$.

The second is also not true. If $z_1=z_2$, then the angle/argument (in terms of polar coordinates) must be the same, meaning the arguments may only differ by a multiply of $2\pi$, not 2 (unless you consider $2\pi$ to be a mutliple of 2).