Find all complex numbers z such that z^2 = 5 + 12i, and give your answer in the form a + bi. Use the square root symbol '√' where needed to give an exact value for your answer. z =
Added by Mary N.
Step 1
The modulus of 5 + 12i is √(5^2 + 12^2) = √169 = 13. The argument of 5 + 12i is arctan(12/5) = 1.176. So, we can write 5 + 12i as 13(cos(1.176) + i*sin(1.176)). Now, we know that if z^2 = 13(cos(1.176) + i*sin(1.176)), then z = ±√13(cos(1.176/2) + Show more…
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