If complex numbers z1- z2 are such that -z1-2- -z2-3 and -z1-z2-5-2-3- then the value of -z1-z2- is

Applying cosine law of triangles in OBC, we get nbsp; cosθ = 3+2 (5 2√(3))2×√(2)×√(3) ⇒cosθ = 1√(2) ⇒θ = π4 ⇒| (z_1) (z_2) |=∠COA=π θ=3π4 ...

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Properties of Argument

If complex nu...

Question

If complex numbers $z_{1}, z_{2}$ are such that $| z_{1} | = \sqrt{2}, | z_{2} | = \sqrt{3} and | z_{1} + z_{2} | = \sqrt{5 - 2 \sqrt{3}}$ , then the value of $| arg (z_{1}) - arg (z_{2}) |$ is

\frac{2 π}{3}

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\frac{π}{3}

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\frac{π}{4}

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\frac{3 π}{4}

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z_{1}, z_{2}

| z_{1} | = \sqrt{2}, | z_{2} | = \sqrt{3} and | z_{1} + z_{2} | = \sqrt{5 - 2 \sqrt{3}}

| arg (z_{1}) - arg (z_{2}) |

z_{1}

z_{2}

| z_{1} | + | z_{2} | = ∣ ∣ ∣ \frac{z_{1} + z_{2}}{2} + \sqrt{z_{1} z_{2}} ∣ ∣ ∣ + ∣ ∣ ∣ \frac{z_{1} + z_{2}}{2} - \sqrt{z_{1} z_{2}} ∣ ∣ ∣

z_{1}, z_{2}, z_{3}

3

\frac{3}{| z_{2} - z_{3} |} = \frac{4}{| z_{3} - z_{1} |} = \frac{5}{| z_{1} - z_{2} |}

\frac{9}{z_{2} - z_{3}} + \frac{16}{z_{3} - z_{1}} + \frac{25}{z_{1} - z_{2}}

z_{1}

z_{2}

z_{3}

\frac{1}{∣ z_{1} - z_{2} ∣} = \frac{3}{∣ z_{2} - z_{3} ∣} = \frac{5}{∣ z_{1} - z_{3} ∣}

\frac{1}{z_{1} - z_{2}} + \frac{9}{z_{2} - z_{3}} + \frac{25}{z_{3} - z_{1}}

z_{1}

z_{2}

z_{1} \neq z_{2}

| z_{1} | = | z_{2} |

\frac{z_{1} + z_{2}}{z_{1} - z_{2}}

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