Question

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

Answer 1

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 .

Consider .

Write the complex number in polar form.

Magnitude is and argument .

Polar form of a complex number is .

Substitute in above form.

De Moivre's theorem:

If is a complex number, then ,

Where is a positive integer.

Find using De Moivre's theorem,.

solution:

(a) Standard form of is .

(b) Standard form of is .