find square root for the complex number - 5 + 12i
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Answered by
4
Answer:
5 – 12i = x2 + 2ixy +(iy)2 = x2 – y2 + 2xyi. => x = ± 3. => y = ± 2. Therefore, √(5 – 12i) = 3 + 2i or, 3 – 2i or, – 3 + 2i or, – 3 – 2i
Answered by
6
Explanation:
Given complex number = 5+12i
The square root of 5+12i is √(5+12i)
Let √(5+12i) = a+ib
On squaring both sides then
=>[√(5+12i)]²=(a+ib)²
=>5+12i=a²+(ib)²+2(a)(ib)
=>5+12i=a²-b²+2abi
(i²=-1)
=>5+12i=(a²-b²)+(2ab)i
On comparing both sides then
=>a²-b²=5 and 2ab=12=>ab=12/2=6
by putting a=3; b=2 then
3²-2²=9-4=5
ab=(3)(2)=6
therefore , a=3 and b=2
now √(5+12i) = a+ib
=>√(5+12i) = 3+2i
and also it is true for a=-3 and b=-2
so, √(5+12i) = 3-2i
√(5+12i) = 3±2i
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