complex numbers help

[latkan]

2.
(a) Find the modulus and argument of -1 - i?3. Hence find (-1 - i?3) ^ 10 in a+ib
form. Find also the square roots of -1 - i?3 in a + ib form.

(b) Use complex numbers to find

? e^-x sin3x dx4.
(a) Find the modulus and argument of z= ?3/2 – (3/2)i. Find (i) z^6 and (ii) the square roots of z

(b) Use complex numbers to find

? e^-kx sin2x dx

Where k is a constant

any help welcome thanks in advance

 

[Deleted member 4993]

2.
(a) Find the modulus and argument of -1 - i?3. Hence find (-1 - i?3) ^ 10 in a+ib
form. Find also the square roots of -1 - i?3 in a + ib form.

Hint:

a+ib can be written as :

\(\displaystyle a \, + ib \, = \, r\cdot e^{i\theta}\)

where:

\(\displaystyle r \, = \, \sqrt {a^2 \, + \, b^2}\)

and

\(\displaystyle \theta \, = \, \tan^{-1}(\frac{b}{a})\)

also

\(\displaystyle [a \, + ib]^n \, = \, [r\cdot e^{i\theta}]^n \, = \, r^n\cdot e^{in\theta}\)

Please show us your work, indicating exactly where you are stuck - so that we know where to begin to help you

(b) Use complex numbers to find

? e^-x sin3x dx4.
(a) Find the modulus and argument of z= ?3/2 – (3/2)i. Find (i) z^6 and (ii) the square roots of z

(b) Use complex numbers to find

? e^-kx sin2x dx

Where k is a constant

any help welcome thanks in advance