- #1

Martin Harris

- 103

- 6

- Homework Statement
- 1) The following vectors are given written as complex numbers:

a = 3-2i

b= -6-4i

c= 4+ 6i

d= -4+3i

The requirements: To calculate the vectors' modulus.

2) The following system of vectors is given

3a-2b=7

-5a+6b=3i

The requirements: To find a and b as vectors, as well as to calculate their modulus.

- Relevant Equations
- Let the vectors be of the following type: z = a+bi, where a = real part, b = imaginary part

Hi

Here is my attempt at a solution for problems 1) and 2) that can be found within the summary.

Problem 1)

a = 3-2i

b= -6-4i

c= 4+ 6i

d= -4+3i

Now, to calculate each vector modulus, I applied the following formula:

$$\left| Vector modulus \right| = \sqrt {(a^2 + b^2) }$$

where a = real part of the vector, and b = imaginary part of the vector

By this formula, the following vector modulus, were calculated:

$$a = \sqrt {13} = 3.605551275463989$$

$$b = 2* \sqrt {13} = 7.211102550927978$$

$$c = 2*\sqrt {13} = 7.211102550927978$$

$$d = \sqrt {25} = 5$$

End of Problem 1 solution attempt

Problem 2)

The following system of vectors is given

$$3a-2b=7 (Eq1)$$

$$-5a+6b=3i (Eq2)$$

I am requested to find vectors a,b as well as to calculate their modulus

From Eq(1), $$ vector a = \frac {7a+2b} {3} Eq (3) $$

Substituting vector a with the above form in Eq 2 yields:

$$vector b = 4.375+1.125i$$ or $$vector b = \frac {35} {8} + \frac {9i} {8} $$

Now plugging back vector b in Eq (3) yields:

$$vector a = 5.25 +0.75i$$ or $$vector a = \frac {15.75} {3} + \frac {2.25i} {3} $$

Now, to calculate the vector modulus, the same formula that was used in Problem1 will be applied, hence it will yield the following vector modulus:

$$Modulus for vector a = \frac {15*\sqrt {2}} {4} = 5.303300858899107 $$

$$Modulus for vector b = 4.517327749898163 $$

End of Problem 2 solution attempt

I would be more than grateful if someone could peer-review (check my attempt).

Many thanks!

Here is my attempt at a solution for problems 1) and 2) that can be found within the summary.

Problem 1)

a = 3-2i

b= -6-4i

c= 4+ 6i

d= -4+3i

Now, to calculate each vector modulus, I applied the following formula:

$$\left| Vector modulus \right| = \sqrt {(a^2 + b^2) }$$

where a = real part of the vector, and b = imaginary part of the vector

By this formula, the following vector modulus, were calculated:

$$a = \sqrt {13} = 3.605551275463989$$

$$b = 2* \sqrt {13} = 7.211102550927978$$

$$c = 2*\sqrt {13} = 7.211102550927978$$

$$d = \sqrt {25} = 5$$

End of Problem 1 solution attempt

Problem 2)

The following system of vectors is given

$$3a-2b=7 (Eq1)$$

$$-5a+6b=3i (Eq2)$$

I am requested to find vectors a,b as well as to calculate their modulus

From Eq(1), $$ vector a = \frac {7a+2b} {3} Eq (3) $$

Substituting vector a with the above form in Eq 2 yields:

$$vector b = 4.375+1.125i$$ or $$vector b = \frac {35} {8} + \frac {9i} {8} $$

Now plugging back vector b in Eq (3) yields:

$$vector a = 5.25 +0.75i$$ or $$vector a = \frac {15.75} {3} + \frac {2.25i} {3} $$

Now, to calculate the vector modulus, the same formula that was used in Problem1 will be applied, hence it will yield the following vector modulus:

$$Modulus for vector a = \frac {15*\sqrt {2}} {4} = 5.303300858899107 $$

$$Modulus for vector b = 4.517327749898163 $$

End of Problem 2 solution attempt

I would be more than grateful if someone could peer-review (check my attempt).

Many thanks!

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