Mathematics: What Ln(z) is answer????!!

What Ln(z) is answer????!! - id6805418, Chrien222

reearamrup27

28.01.2022

Write z in exponential form:

$z=1-i=\sqrt2 e^{-i\frac\pi4}$

Then taking the logarithm, we get

$\mathrm{Ln}(z)=\ln(\sqrt2) + \ln e^{-i\frac\pi4} = \boxed{\ln(\sqrt2)-\dfrac\pi4i}$

so a is the correct answer.

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mathhelppls14

02.02.2023

Step 1: Use the slope formula y₂ - y₁/x₂ - x₁ to find the slope.

$\frac{0 - (-4)}{-3 - 3}\\ \\\frac{4}{-6} = -\frac{2}{3}$

Step 2: Plug the slope we found and one point into the slope-intercept formula, y = mx + b.

$y = mx + b\\\\0 = -\frac{2}{3}(6) + b\\\\0 = -4 + b\\\\4 = b$

Step 3: Put it all together.

$y = -\frac{2}{3}x + 4$

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