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Find the value of k for the equation 2k2 + 144 = 0

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  • Last Updated : 07 Feb, 2022
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Complex numbers are those with the formula a + ib, where a and b are real numbers and I (iota) is the imaginary component and represents (-1), and are often represented in rectangle or standard form. 10 + 5i, for example, is a complex number in which 10 represents the real component and 5i represents the imaginary part. Depending on the values of a and b, they might be wholly real or purely fictitious. When a = 0 in a + ib, ib is a totally imaginary number, and when b = 0, we get a, which is a strictly real number.

Some Powers of i

  • i = \sqrt{-1}
  • i2 = −1
  • i3 = i × i2 = i × −1 = −i
  • i4 = i2 × i2 = −1 × −1 = 1

Find the value of k for the equation 2k2 + 144 = 0.

Solution:

2k2 + 144 = 0

⇒ 2k2 = −144

⇒ k2 = −72

⇒ k = \sqrt{-72}

⇒ k = \sqrt{-(1)(2)(6)(6)}

⇒ k = 6\sqrt{2}\sqrt{-(1)}

⇒ k = 6√2i

Similar Problems

Question 1. Find k if 2k2 + 64 = 0.

Solution:

2k2 + 64 = 0

⇒ 2k2 = −64

⇒ k2 = −32

⇒ k = \sqrt{-32}

⇒ k = \sqrt{-(1)(2)(4)(4)}

⇒ k = 4\sqrt{2}(\sqrt{-1})

⇒ k = 4√2i

Question 2. Find k if 2k2 + 36 = 0.

Solution:

2k2 + 36 = 0

⇒ 2k2 = −36

⇒ k2 = −18

⇒ k = \sqrt{-18}

⇒ k = \sqrt{-(1)(2)(3)(3)}

⇒ k = 3\sqrt{2}(\sqrt{-1})

⇒ k = 3√2i

Question 3. Find k if 2k2 + 400 = 0.

Solution:

2k2 + 400 = 0

⇒ 2k2 = −400

⇒ k2 = −200

⇒ k = \sqrt{-200}

⇒ k = \sqrt{-(1)(2)(10)(10)}

⇒ k = 10\sqrt{2}(\sqrt{-1})

⇒ k = 10√2i

Question 4. Find k if 2k2 + 100 = 0.

Solution:

2k2 + 100 = 0

⇒ 2k2 = −100

⇒ k2 = −50

⇒ k = \sqrt{-50}

⇒ k = \sqrt{-(1)(2)(5)(5)}

⇒ k = 5\sqrt{2}(\sqrt{-1})

⇒ k = 5√2i

Question 5. Find k if 2k2 + 256 = 0.

Solution:

2k2 + 256 = 0

⇒ 2k2 = −256

⇒ k2 = −128

⇒ k = \sqrt{-128}

⇒ k = \sqrt{-(1)(2)(8)(8)}

⇒ k = 8\sqrt{2}(\sqrt{-1})

⇒ k = 8√2i

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