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Milly
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View attachment 4273Helppp for part (ii). I got 3$e^{\frac{1}{6}\theta i}$
The two square roots of $re^{\theta i}$ are $\sqrt re^{\frac12\theta i}$ and $\sqrt re^{(\frac12\theta+ \pi) i}$.Milly said:
Finding two square roots of z is the process of determining two numbers that, when multiplied by themselves, equal the given number z.
Knowing the two square roots of z can be useful in various mathematical applications, such as solving quadratic equations or finding the length of one side of a right triangle.
To find the two square roots of z, you can use the square root property which states that if the square of a number equals z, then the number itself is a square root of z. You can also use the quadratic formula for more complex equations.
Yes, there can be multiple square roots of z, but when referring to "finding two square roots of z," it implies finding the two distinct and unique square roots.
If z is a negative number, it is still possible to find two square roots. However, they will be imaginary numbers, and the process of finding them is slightly different. It involves using the concept of imaginary numbers and the complex number system.
