Find the square root of -15 -8i

1.	Find the square root of -15 -8i
Answer» Let {tex}x + yi = \\sqrt { - 15 - 8i} {/tex}Squaring both sides, we get(x + yi)2 = -15 - 8ix2 - y2 + 2xyi = -15 - 8iComparing the real and imaginary partsx2 - y2 = -15 .... (i){tex}2xy = - 8 \\Rightarrow xy = - 4{/tex}Now, we know that(x2 + y2)2 = (x2 - y2) + 4x2y2= (-15)2 + 4(-4)2= 225 + 64= 289{tex}\\therefore {x^2} + {y^2} = 17{/tex}\xa0..... (ii) [Neglecting (-) sign as x2 + y2 > 0]Solving (i) and (ii), we get{tex}x = \\pm 1{/tex}\xa0and {tex}y = \\pm 4{/tex}Since the sign of xy is (-){tex}\\therefore{/tex}\xa0x = 1, y = -4And x = -1, y = 4{tex}\\therefore \\sqrt { - 15 - 8i} = \\pm (1 - 4i){/tex}<br>Answer is 1-4i

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