Posted by **Queenie** on Monday, September 23, 2013 at 10:59pm.

1)

i) use an algrbraic method to find the square root of 2+i√5. give your answer in the form x+iy, where x and y are exact real numbers

ii)hence find in the form x+iy where x and y are exact real numbers, the roots of the equation z^4-4z^2+9=0

iii) show those roots on an argand diagram (part ii)

iv) given that α is a root of the equation in part (ii) such that 0< or equal to argα< or equal to π/2, sketch on the same argand diagram the locus of |z-α|=|z|

- Pure Mathematics -
**Steve**, Tuesday, September 24, 2013 at 12:39am
2+i√5 = 1/4 (8+4i√5) = 1/4 (10+4i√5-2) = 1/4 (√10+i√2)^2

so √(2+i√5) = 1/2 (√10+√2i)

The rest should fall right out.

- Pure Mathematics -
**Anonymous**, Tuesday, September 24, 2013 at 6:11pm
I don't understand how you got any of that =(

- Pure Mathematics -
**Queenie**, Tuesday, September 24, 2013 at 10:41pm
where'd the 1/4 and all that come from?

## Answer This Question

## Related Questions

- Math PLEASE HELP ASAP - -PLEASE INCLUDE SOLUTIONS AND EXPLAIN HOW YOU DID IT ...
- algebra - 1)Write the expression 9n^6+7n^3-6 in quadratic form,if possible A.9(n...
- Math(I Don't Get THIS!!) - 15sqrt8x^16/5sqrt2x^4 *I totally need help with this ...
- Math - i^6 = (i^2)^3 = (-1)^3 = -1 The square, not the square root of -1 is 1...
- Algebra - Express the following in simplest radical form. All variables ...
- MATH - 1. Rosa, Roberto, Andrea, and Inno find an estimate for square root 10. ...
- Algebra - Use the quadratic formula to solve the equation. Give exact answers: ...
- algebra - 1.)correct 2.)wrong---> the first term is wrong 4(3a^2)^2 = 36a^4 3...
- Math - find the value of k in simplest form for which the larger root of x^2-5x+...
- algebra - Help Fast PLEASE!! check for corrections on my problems 1.Rewrte the ...

More Related Questions