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Cosine Rule

if z=4+3√(20)...

Question

if z=4+3\sqrt{20}i, i=\sqrt{-1}, then the positive value of {(\sqrt z+\sqrt{\overline z} )}^2 is equal to

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| z_{i} | = i, i = 1, 2, 3, 4

| 16 z_{1} z_{2} z_{3} + 9 z_{1} z_{2} z_{4} + 4 z_{1} z_{3} z_{4} + z_{2} z_{3} z_{4} | = 48,

then the value of

∣ ∣ ∣ \frac{1}{{¯ ¯ ¯ z}_{1}} + \frac{4}{{¯ ¯ ¯ z}_{2}} + \frac{9}{{¯ ¯ ¯ z}_{3}} + \frac{16}{{¯ ¯ ¯ z}_{4}} ∣ ∣ ∣ .

| z - 1 | = 2

, then the value of

z ¯ ¯ ¯ z - z - ¯ ¯ ¯ z

z = 4 - 3 \sqrt{2} i

then the value of

z ¯ ¯ ¯ z =

z_{1}, z_{2}

are complex numbers, then the maximum value of

\frac{z_{1}_{2} +_{1} z_{2} + z_{1} z_{2} +_{1}_{2}}{| z_{1} z_{2} |}

z

is a complex number and

¯ ¯ ¯ z

is conjugate of

z

(1 + i) z = (1 - i) ¯ ¯ ¯ z,

then the value of

z + i ¯ ¯ ¯ z

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