Question

Find the square root of 16+30i

Answer 1

Answer:

it's ans is -63ivhhhgghh

Answer 2

Answer:

AccordingtotheQuestion

Assumption

√16 - 30i = (x + iy) ..... (1)

\textbf{\underline{Squarring\;both\;sides :-}}

Squarringbothsides :-

(16 - 30i) = (x - iy)²

(16 - 30i) = (x² - y²) - i(2xy) ... (2)

Here

\Large{\boxed{\sf\:{Real\;and\;imaginary\;part\;of\;both\;sides\;of\;(2)}}}

Realandimaginarypartofbothsidesof(2)

(x² - y²) = 16

2xy = 30

(x² + y²) = √{(x² - y²)² + 4x²y²}

= √(16² + 30²)

= √(256 + 900)

= √1156

= 34

Hence,

(x² - y²) = 16 .... (3)

Also,

(x² + y²) = 34 ..... (4)

\Large{\boxed{\sf\:{Solving\;(3)\;and\;(4)}}}

Solving(3)and(4)

x² = 25

x = √25

x = ±5

Also,

y² = 9

y = √9

y = ±3

Here

xy > 0

Therefore,

(x = 5 and y = 3) or (x = -5 and y = -3)

Hence,

√16 - 30i = (5 - 3i) or (-5 + 3i)