Question

please solve this problem and answer in steps​

Answer 1

Answer:

A) ±1/√2(5 - 3i)

Step-by-step explanation:

Let us say square root of complex number 8-15i is

a + ib

then squaring it

a² + i²b² + 2abi

a² - b² + 2abi

comparing with

8 - 15i

a²-b² = 8

2ab = - 15

b = -15/2a

a² - (-15/2a)² = 8

4a⁴ - 225 = 32a²

4a⁴ -32a² - 225 = 0

4a⁴ - 50a² + 18a² - 225 = 0

2a²(2a² - 25)+9(2a² - 25) = 0

(2a² + 9) (2a² - 25) = 0

a² = -9/2. or a² = 25/2

a = 3i/√2 ; a = 5/√2

b = -5i/√2;  b = -3/√2

a + ib = (5 - 3i)/√2

or

a + ib = (3i - 5)/√2

i.e. ±1/√2(5 - 3i)