find the roots of the equation z^2=21-20i, how are they related in the argand diagram

  • 0 votes

Could you also show how you worked it out please

Posted Wed 24th October, 2012 @ 20:19 by SS

2 Answers

  • 1 vote

z= (a+bi)

(a+bi)(a+bi) = 21 - 20i

(a^2)+(2abi)+(b^2 x i^2) = 21 - 20i

(a^2)+(2abi) - b^2 = 21 - 20i

Equate real parts: a^2-b^2 = 21

Equate imaginary parts: 2ab = 20

Then solve simultaneously.

The answers will be (a+bi) and (a-bi), so on an argand diagram they will be reflections in the x axis.

Answered Sun 11th November, 2012 @ 16:12 by Sarah V
  • 0 votes

Ahh thank you so much :)

Answered Mon 12th November, 2012 @ 07:42 by SS