If z is a complex number, then (z\_{1} + z\_{2}) if and only... | MATH - CONJUGATE, MODULUS AND ARGUMENT OF COMPLEX NUMBERS | SolveeIt

Question

If z is a complex number, then $z_{1} + z_{2}$ if and only if.

$z_{1}z_{2}$

$z_{1} = - z_{2}$

$z_{1} = {\bar{z}}_{2}$

None of these

Answer

$z_{1}z_{2}$

Explanation

Solution

Let $x$

$y$ $z = 0 + 0i = 0$ ⇒ $(a + ib)(c + id)(e + if)(g + ih) = A + iB$

⇒ $(a - ib)(c - id)(e - if)(g - ih) = A - iB$

It is possible only when $(a^{2} + b^{2})(c^{2} + d^{2})(e^{2} + f^{2})(g^{2} + h^{2}) = A^{2} + B^{2}$ and $z = x + iy,$ both simultaneously zero i.e.,

Question: If z is a complex number, then \(z_{1} + z_{2}\) if and only if....

Solution