Evaluate each of the following in x+iyform, and compare with a computer solution.

ln(-i)

Short Answer

Expert verified

Thex+iy form of the given equationln(-i) is3π2i .

Step by step solution

01

Given Information.

The given expression isln(-i) .

02

Meaning of rectangular form.

Represent the complex number in rectangular form means writing the given complex number in the form ofx+iy in which x is the real part and y is the imaginary part.

03

Convert in polar form.

Consider, z=-i.

Write the polar form of the number.

z=reiθ

The angle is located in negative imaginary axis so the angle must be accordingly.

r=-ir=1θ=3π2

Put the values in the polar form.

z=e3π2i

04

Write in the form of x+iy .

Convert the polar form into the rectangular form.

z=reθilnz=ln(r)+lneθiln(-i)=ln(1)+3π2ilne

Therefore,x+iythe form of the given equation (-i)is 3π2i.

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