Class 11Mathematics1 Complex Numbers and Quadratic Equations: Complex NumbersMix Examples-Complex numbers
DifficultLet $Z$ and $W$ be complex numbers such that $|Z| = |W|$,and $\text{arg } Z$ denotes the principal argument of $Z$.
Statement $1$: If $\text{arg } Z + \text{arg } W = \pi$,then $Z = -\overline{W}$.
Statement $2$: $|Z| = |W|$ implies $\text{arg } Z - \text{arg } \overline{W} = \pi$.
Statement $1$: If $\text{arg } Z + \text{arg } W = \pi$,then $Z = -\overline{W}$.
Statement $2$: $|Z| = |W|$ implies $\text{arg } Z - \text{arg } \overline{W} = \pi$.
- AStatement $1$ is true,Statement $2$ is false.
- BStatement $1$ is true,Statement $2$ is true,Statement $2$ is a correct explanation for Statement $1$.
- CStatement $1$ is true,Statement $2$ is true,Statement $2$ is not a correct explanation for Statement $1$.
- DStatement $1$ is false,Statement $2$ is true.
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Similar Questions
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DifficultTS EAMCET 2002
View SolutionLet $\omega = e^{i \pi / 3}$,and $a, b, c, x, y, z$ be non-zero complex numbers such that $a+b+c = x$,$a+b \omega + c \omega^2 = y$,and $a+b \omega^2 + c \omega = z$. Then the value of $\frac{|x|^2+|y|^2+|z|^2}{|a|^2+|b|^2+|c|^2}$ is
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