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timurjin [86]
2 years ago
15

What is the other square root of 119 + 120i?

Mathematics
1 answer:
MakcuM [25]2 years ago
8 0

Answer:

\sqrt{119+120 i}=\pm (12.24+i 4.90)

Step-by-step explanation:

Given

z = 119 + 120 i

Let \sqrt{119+120 i}=p+iq

Squaring both sides

119+120 i=p^2-q^2+2ipq

Comparing real and imaginary part

Re(LHS)=Re(RHS)

119=p^2-q^2...........................(1)

comparing Im(LHS)=Im(RHS)

120=2pq

q=\frac{60}{p}

Substitute q in 1

119=p^2-(\frac{60}{p})^2

p^4-119p^2-(68)^2=0

Let x=p^2

x^2-119x-4624=0

x=\dfrac{119\pm \sqrt{119^2+4\times 4624}}{2}

x=\frac{119\pm 180.71}{2}

we take only Positive value because p^2=x

x=149.85  

p^2=149.85

thus p=\pm 12.24

q=\pm 4.90

thus,

\sqrt{119+120 i}=\pm (12.24+i 4.90)

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