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Polar form complex numbers

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Perform operatins using the complex numbers below. Uses polar form and give all angles in radians in the interval  [0,2pi)

z1=1-i

z2=-i

a) z1z2=re^ie where r=________ and theta =_______

b) z1/z2=re^io where r=_______ and theta =_________
asked Jul 7, 2016 in PRECALCULUS by anonymous
reshown Jul 8, 2016 by goushi

1 Answer

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Step 1:

The complex numbers image.

Write the complex number in polar form.

Substitute image and imagein the polar form.

image

The argument is image.

image

Hence, the polar form of complex numbers image

Step 2:

(a)

image Find image.

Eulerimages formula: image.

Substitute image

image

Since, image

(b)

image Find image.

Eulerimages formula: image.

Substitute image

image

Since, image

Solution:

image

image

answered Jul 8, 2016 by Anney Mentor

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