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March 30, 2015

March 30, 2015

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

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 12:39am2+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 6:11pmI don't understand how you got any of that =(

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

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