Which Number is Largest? (Complex Numbers)?

Question

a) 3i
b) -7
c) 4
d) -2i
e) 4+4i

Answer 1

Complex numbers are unordered. There is no largest. -7 has the largest modulus but this is not the same thing as being the largest.

Answer 2

Answer: b) -7+0i
has max distance from origin.


a) 0+3i
r=3

b) -7+0i
r=7

c) 4+0i
r=4

d) 0-2i
r=2

e) 4+4i
r=sqrt(32)

Answer 3

I suppose 4 is the largest because -7 is definitely below 4 and the rest are imaginary numbers. Imaginary numbers don't actually have a value.

Answer 4

since i is a positive number than the answer is 4+4i is the largest number. imaginary numbers don't have a definite value but they can be compared with other numbers of course

Answer 5

With complex numbers you cannot specify that z1>z2. you can specify that |z1|>|z2|.

If you are talking about the largest value of |z| given the above possible values of z, the largest value would be with z=-7. in this case |z| = 7

a) |z |= 3
b) |z| = 7
c) |z| = 4
d) |z| = 2
e) |z| = 5.66 (approx)

Largest value of |z| = 7 ---- (b)

Answer 6

On the complex plane, contrarily to the real line, there's no order relation, so it doesn't make sense to say a complex number is larger than another.