Question

A) I-2,8I - I-1,3IБ) I12,8I + I-1,3I​

Answer 1

1) |-2,8|-|-1,3|= 2,8-1,3= 1,5

2) |12,8|+|-1,3|=12,8+1,3= 14,1

Answer 2

Let's simplify the given expressions step by step:

A) I-2,8I - I-1,3I

First, let's interpret the notation: Ia,bI represents the absolute value of the complex number a + bi.

So, I-2,8I means the absolute value of the complex number -2 + 8i, and I-1,3I means the absolute value of the complex number -1 + 3i.

Now, calculate each absolute value: I-2,8I = |-2 + 8i| = sqrt((-2)^2 + (8)^2) = sqrt(4 + 64) = sqrt(68) = 2*sqrt(17)

I-1,3I = |-1 + 3i| = sqrt((-1)^2 + (3)^2) = sqrt(1 + 9) = sqrt(10)

Now, the expression becomes: 2*sqrt(17) - sqrt(10)

This is the simplified form of the expression A.

B) I12,8I + I-1,3I

Again, let's interpret the notation: Ia,bI represents the absolute value of the complex number a + bi.

So, I12,8I means the absolute value of the complex number 12 + 8i, and I-1,3I means the absolute value of the complex number -1 + 3i.

Now, calculate each absolute value: I12,8I = |12 + 8i| = sqrt((12)^2 + (8)^2) = sqrt(144 + 64) = sqrt(208) = 4*sqrt(13)

I-1,3I = |-1 + 3i| = sqrt((-1)^2 + (3)^2) = sqrt(1 + 9) = sqrt(10)

Now, the expression becomes: 4*sqrt(13) + sqrt(10)

This is the simplified form of the expression B.