No, It is the product of the modulus of z and z itself, you are to solve.

Mathematics

ScanSolve AI Answer

Answer

23+2i2\sqrt{3} + 2i

Step-by-step solution

2 steps

You are correct that we can calculate the product of the modulus of zz and zz itself. However, the image for question 85 explicitly asks for z5z^5.

Let's calculate the product of the modulus of zz and zz itself, as you requested.

  1. Find the modulus of zz.

    Given z=3+iz = \sqrt{3} + i.
    The modulus rr is:

    r=∣z∣=(3)2+(1)2=3+1=4=2r = |z| = \sqrt{(\sqrt{3})^2 + (1)^2} = \sqrt{3 + 1} = \sqrt{4} = 2
  2. Calculate the product of ∣z∣|z| and zz.

    ∣z∣⋅z=2⋅(3+i)|z| \cdot z = 2 \cdot (\sqrt{3} + i) ∣z∣⋅z=23+2i|z| \cdot z = 2\sqrt{3} + 2i

    This result, 23+2i2\sqrt{3} + 2i, does not match any of the options provided for question 85 in the image (A. 2, B. 3+i3+i, C. 3−i3-i, D. 4).

    As previously calculated, if the question is indeed asking for z5z^5:

    z5=−163+16iz^5 = -16\sqrt{3} + 16i

    This also does not match any of the given options.

    The final answer for the product of the modulus of zz and zz itself is 23+2i\boxed{2\sqrt{3} + 2i}.

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