Imaginary Numbers, and such.?

Question

Just a few that I need help with.

1. 3i+4i
2. 2i-5i
3. sqroot(-16)-sqroot(-9)
4.sqroot(-25)*sqroot(-4)
5. (-7i)*-i
6. sqroot(-4/9)*sqroot(-64/25)

Answer 1

1. 3i + 4i = 7i
2. 2i - 5i = -3i
3. sqrt(-16)-sqrt(-9) = sqrt(-1)*sqrt(16) - sqrt(-1)*sqrt(9) =
= 4i - 3i = i
4 sqrt(-25)*sqrt(-4) = i*sqrt(25)*i*sqrt(4) = i*i*sqrt(25*4) =
= -sqrt(100) = -10

5. (-7i)*(-i) = i*(-7)*i*(-1) = i*i*(-1)*(-7) = -1*7=-7

6. sqrt(-4/9)*sqrt(-64/25) = 2i/3 * 8i/5 = -16/15

Answer 2

the 1st 2 solutions are idiotic solutions. Imaginary numbers are used each and every of the time interior the genuine worldwide, incredibly in electric engineering, civil engineering, mechanical engineer, and utilized physics. complicated numbers enable modifications that make particularly complicated calculations trival. An engineer used complicated equations to make each and every thing you may become attentive to - your pc, your television, your vehicle, each and every thing. it is precisely merely like using multiplication and addition. you utilize the guidelines of multiplication to remedy a situation like 6 * 8793, as a results of fact multiplying is infintely much less complicated than including six to itself 8793 circumstances. no one might say you do no longer use multiplication interior the genuine worldwide as a results of fact it makes repetitive including simplier. it somewhat is actual, in spite of the undeniable fact that, that throughout the time of contrast to multiplication which you utilize daily in straight forward initiatives, while you're no longer in a technical field or easily utilizing math to remedy actual complications you will probable by no ability use imaginary numbers.

Answer 3

i = sqrt of -1 since this term is usually term undefined in the set of real numbers it is defined as i.

1. 7i
2. -3i
3. 4i-3i
4. 10
5. -7
6. -16/15