SOLUTION: This question came from an exam paper in Australia: Solve: z^2=3+5i I presume that the question requires an answer in the form z = a + bi I have tried, but I end up getting a sq

Question 189153: This question came from an exam paper in Australia:
Solve: z^2=3+5i
I presume that the question requires an answer in the form z = a + bi
I have tried, but I end up getting a square root of a square root for an exact answer, or approx. +1.1897 or -1.1897 for b and approx. +2.1013 or -2.1013 for a.
I obtained this by letting z = a + bi, and therefore z^2 = a^2 + 2abi -b^2, and therefore a^2 - b^2 equals 3, and 2ab equals 5, and then solving these two simultaneous equations.
Is there a simpler way, please?

Answer by Alan3354(69443) (Show Source): You can put this solution on YOUR website!
Use the Argand diagram.
--> = (34)^(1/4)cis(29.52)
= ~ 2.415cis(29.52)

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