complex numbers?

Question

z1=3+j2 and z2=4-j3

find |z1-z2|


could you provide a detailed answer

needs to be to three dp. my solution says its 5.099

Answer 1

To subtract complex numbers we subtract the two real parts and the two imaginary parts
so z = z1 - z2
gives z = (3 - 4) + (2 - (-3))j ← Thomas had an error here!
therefore z = -1 + 5j

The modulus of a complex number is given as
|z| = √(x^2 + y^2)
where x is the real part and y is the imaginary part

So we have
|z| = √( (-1)^2 + 5^2)
|z| = √(1 + 25)
|z| = √(26)
|z| = 5.099

Another way to "see" the answer would be to create a line segment joining the two points Then, create a right tringle using horizontal and vertical line segments of length 1 and 5, respectively. The hypotenuse would then be √(26) ≈ 5.099.

Answer 2

The question is: z1=3+j2 and z2=4-j3 find |z1-z2|
Answer:
j = square root of minus 1, bar signs mean absolute value

putting the values of z1 and z2 together, we get:
z1 - z2 = absolute value of (3+j2) - (4-j3)
= absolute value of 3 + j2 - 4 + j3
= absolute value of (3 -4) + j (2+3)
= absolute value of -1 + j5

since the value of (minus one under root) can not be added or subtracted
from a regular number, thus we have to find the absolute values of
these two elements separately and add them together. As such

= absolute value of -1 = +1,
and absolute value of +j5 = +j5

The answer is sum of these two values: that is +1+j5 or 1+j5

Done !!!!

Answer 3

To subtract complex numbers we subtract the two real parts and the two imaginary parts
so z = z1 - z2
gives z = (3 - 4) + (2 - 3)j
therefore z = -1 + (-1j)

The modulus of a complex number is given as
|z| = sqrt(x * x + y * y)
where x is the real part and y is the imaginary part

So we have
|z| = sqrt( (-1 * -1) + (-1 * -1))
|z| = sqrt (1 + 1)
|z| = sqrt(2)
|z| = 1.414213562 or -1.141213562

Answer 4

z1 - z2 = (3 + j2) - (4 - j3)

The numbers with 'j' are called imaginary part of complex number. The numbers without the 'j' element is the real part.

We subtract the real and imaginary parts seperately.

z1 + z2 = (3 - 4) + (j2 - (-j3)) = -1 + (j2 + j3) = -1 + j5

Now, the modulus of z1-z2 is:
|z1 - z2| = square root of (square of real part + square of imaginary part)

|z1 - z2| = square root of (1 + 25) = square root of 26 = 5.099.

If you still haven't got it, mail me at [e-mail] for more detailed explanations.

Answer 5

3

Answer 6

|z1 - z2| =
|(3 + j^2) - (4 - j^3)| =
|3 + j^2 - 4 + j^3| =
|j^3 + j^2 - 1|

for a graph, go to www.quickmath.com, click Plot under Equations, type your problem in as y = |x^3 + x^2 - 1|, change the margins to

-10,10
-10,10

then click plot.

Answer 7

z1 - z2 = (3+j2)-(4-j3) = -1 + j5, the magnitude of this is sqrt (1^2 + 5^2) or sqrt 26, which is roughly 5.099