Question

Write the expression i^(-55) in the form of a+bi where a and b are real numbers

Answer 1

i^55 means \[\frac{1}{i^{55}}\] if we multiply numerator and denominator by i we have \[\large \frac{i}{i^{56}}\] since i^2 = -1 we rewrite as \[\Large \frac{i}{(-1) ^{28}} = i\]

Answer 2

i *guess* a + bi form would be \[0 + 1i\] or just i?

Answer 3

@lgbasallote The book leaves out the zero but I have been putting it just to be sure, so when solving problems with negative exponents how would you know what to do when you add three and multiply by i^58 and isn't a multiple of 4?

Answer 4

i cant understand your problem o.O mind giving an example?

Answer 5

Like how if you had i^-33 and you would solve this by saying i^-33*i^-36 = i^3 = -i