# maths/ physics

posted by .

Determine the two square roots of 3+j4 in both a)Cartesian form
b) Polar form

Any help with this question would appreciated

• maths/ physics -

let the angle be Ø
then r = √(3^2+4^2) = 5
tanØ = 4/3, Ø = .9273

3 + 4j = 5(cos .9273 + jsin .9273)
by De Moivre's theorem

(3 + 4j)^(1/2) = √5(cos ((1/2).9273) + jsin ((1/2).9273))

= √5( cos .4636 + jsin .4636)

or 2 + j if expanded.

check:
if 2+j is the square root of 3+4j, then
(2+j)^2 should equal 3+4j

Left side = (2+j)^2
= 4 + 4j + j^2
= 4 + 4j - 1
= 3 + 4j

so √(3+4j) = 2+j or √5(cos .4636 + jsin .4636)

## Similar Questions

1. ### Pre-Cal

Find the 5 roots of x^5+1=0 in polar and Cartesian form. (x^5 means x to the 5th power) x^5 = -1 = e^[i (2n + 1) pi] where i is any integer x = [e^[i (2n + 1) pi]]^(1/5) = e^(i pi/5)= cos pi/5 + i sin (pi/5) = e^(3 i pi/5) = cos (2 …
2. ### calculus

for what value of r=4sinè have vertical tangent?
3. ### Maths - Polar Coordinate Systems

I've received an assignment to investigate the polar coordinate system compared to the cartesian one. Theres a question that asks you to investigate into how to convert polar coordinates into cartesian. From my text book, I know in …
4. ### Math 12

Hey everyone; There are some questions on my review I am having trouble with. 4. Evaluate each logarithm. g)log base 5 square root 5 I can't figure out how to do square roots... h)log base 3 1 I got 3, but the anwser is 0 Also, directions …
5. ### Precalculus

"Show that x^6 - 7x^3 - 8 = 0 has a quadratic form. Then find the two real roots and the four imaginary roots of this equation." I used synthetic division to get the real roots 2 and -1, but I can't figure out how to get the imaginary …
6. ### precalculus

Let z1= 3-3sqrt 3i and z2= -11+i. write all answers in polar form with 0< theta< 2pi A. what is z1 in polar form?
7. ### precalculus

Let z1= 3-3sqrt 3i and z2= -11+i. write all answers in polar form with 0< theta< 2pi A. what is z1 in polar form?
8. ### Maths

Have a question on complex numbers. Z1= 1+j2, Z2= 2+j5 Find total impedance in Cartesian and polar form of two impedances in parallel: 1/ZT = 1/Z1 + 1/Z2 I get to 39/58 + 83/58 j but then get a bit lost.
9. ### Pre-calculus- URGENT

Convert the rectangular coordinate (-8,i (square root of 3) into polar coordinates. How do I do this?
10. ### Maths

Convert the complex no. In polar form : 1-i rcosΘ =1 rsinΘ=-1 r=√a2+b2 r=√(1)2+(-1)2 r=√2 TanΘ=b/a =1/-1 =-1 After all this what i have to do to find out value of Θ?

More Similar Questions