Find the square roots of each complex number.
a. 5 + 12i
b. 5 − 12i

ANSWER:

Square root of 5 + 12i is 3+2i or -3 – 2i and square root of 5 – 12i is 3 – 2i or -3 + 2i.

SOLUTION:

Given, we have to find square roots of 5 + 12i and 5 – 12i

a) 5 + 12i

Now, square root of 5 + 12i  

Suppose that a + bi is a square root of 5 + 12i.  

Equate real and imaginary parts:

Since a must be real, a = 3 or -3.  

This gives b = 2 or -2, respectively.  

Thus, we have two square roots: 3+2i or -3-2i.

b) 5 - 12i

Now, square root of 5 - 12i  

Suppose that a - bi is a square root of 5 - 12i.  

Equate real and imaginary parts:

This gives b = 2 or -2, respectively.  

Thus, we have two square roots: 3 - 2i or -3 + 2i.

Hence, square root of 5 + 12i is 3+2i or -3 – 2i and square root of 5 – 12i is 3 – 2i or -3 + 2i.

answer

explanation

the area of a circle is calculated using the formula

or

we can use any of the above formulae to calculate the required. preferably, let us use the latter since the diameter is

we substitute the diameter into the formula to get:

this is the exact value for the area of the circle.

the correct answer is a

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step-by-step explanation: