how do you do this? imaginary numbers?

Question

if the problem was i^18
would it be
i or -i???


The area of a room is "5" and the length is "1+2i". What is the width of the room?



The conjugate of the complex number "3+2i" is?



What is the meaning of "i"?

-1

sqrt -1

sqrt 1

1


i will award a best answer
thakn you so much for helping me before my big test

Answer 1

Note these things: i = sqrt(-1), i^2 = -1, i^3 = (i^2)*i = (-1)*i = -i, and i^4 = (i^2)*(i^2) = 1. After that, powers of i simply repeat. For example, to find i^22, we first notice that 22 = 4*5 + 2, so i^22 = ((i^4)^5)*(i^2) = (1^5)*(i^2) = -1.

For the next one you want to divide 5 by 1 + 2i as follows. To divide by the complex number 1 + 2i, multiply 5/(1 + 2i) numerator and denominator by 1 - 2i (which is the conjugate of 1 + 2i). We have 5*(1 - 2i)/[(1 + 2i)*(1 - 2i)] = (5 - 10i)/(1 + 2i - 2i - 4i^2). The denominator is 1 - 4i^2 = 1 - 4*(-1) = 5. Therefore, the answer is (5 - 10i)/5 = 1 - 2i.

As in the last example, the congujate of a + bi is a - bi.

Good luck.

Answer 2

i^4=i^2*i^2=1 so i^18 = i^16*i^2=-1
It does not make sense to express widh and length as complex numbers
In any case the are asking you to find 5=(1+2i)*(x+i y)so
5= x+iy+2xi -2y = (x-2y) +i( 2x+y)
2x+y=0
x-2y=5 so y = -2x and 5x=5 so x = 1 and y = -2
x+iy=1-2i
The conjugate is 3-2i
i=sqrt(-1)
You should study for your homework or test