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Evaluate and write the answer in standard form a) 4+10i/3-4i b)i^26?

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Evaluate and write the answer in standard form a) 4+10i/3-4i b)i^26?

asked Feb 10, 2015 in PRECALCULUS by anonymous

1 Answer

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Step 1:

(a) The complex number is.

Standard form of a complex number is .

Multiply the numerator and denominator by .

Standard form of is .

Step 2:

(b) The complex number is image.

Consider .

Write the complex number in polar form.

Magnitude is and argument .

Polar form of a complex number is .

Substitute in above form.

image

De Moivre's theorem:

If is a complex number, then image,

Where image is a positive integer.

Find image using De Moivre's theorem,.

image

image

solution:

(a) Standard form of is .

(b) Standard form of image is image.

answered Feb 10, 2015 by cameron Mentor

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