If z 1 - 2 -2 1 - i and z - 1 - i -3- then z12 z23 is equal to

The correct option is E 128 i Given, z_1=2√(2)(1+i), z_2=1+i√(3) Therefore, z_1^2=8(1+i)^2 =8(1+2i 1) =16i and z_2^3=(1+i√(3))^ ...

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Complex Numbers

If z 1 = 2 ...

Question

If $z_{1} = 2 \sqrt{2} (1 + i)$ and $z = 1 + i \sqrt{3}$ , then $z_{1}^{2} z_{2}^{3}$ is equal to

128 i

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64 i

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- 64 i

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- 128 i

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256

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Solution

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Similar questions

z_{1} = (2 - i)

z_{2} = (1 + i),

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

$If z + x + i y then (z) = \sqrt{x^{2} + y^{2}} z_{1} = 2 - i, z_{2} = 1 + i, find ∣ ∣ \frac{z_{1} + z_{2} + 1}{z_{1} - z_{2} + i} ∣ ∣ .$

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

| z | = 2

z_{1} = 1 + i \sqrt{3}

z_{2}

z_{3}

arg ⎛ ⎜ ⎜ ⎜ ⎝ \frac{z_{1} - \frac{z}{| z |}}{\frac{z}{| z |}} ⎞ ⎟ ⎟ ⎟ ⎠ = \frac{π}{2}

∣ ∣ ∣ \frac{z}{| z |} - z_{1} ∣ ∣ ∣ = 3

| z_{1} |^{2}

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