# Find the value of k for the equation 2k^{2} + 144 = 0

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 =
- i
^{2}= −1- i
^{3}= i × i^{2}= i × −1 = −i- i
^{4}= i^{2}× i^{2}= −1 × −1 = 1

**Find the value of k for the equation 2k**^{2} + 144 = 0.

^{2}+ 144 = 0.

**Solution:**

2k

^{2}+ 144 = 0⇒ 2k

^{2}= −144⇒ k

^{2}= −72⇒ k =

⇒ k =

⇒ k =

⇒ k = 6√2i

**Similar Problems**

**Question 1. Find k if 2k ^{2} + 64 = 0.**

**Solution:**

2k

^{2}+ 64 = 0⇒ 2k

^{2}= −64⇒ k

^{2}= −32⇒ k =

⇒ k =

⇒ k =

⇒ k = 4√2i

**Question 2. Find k if 2k ^{2} + 36 = 0.**

**Solution:**

2k

^{2}+ 36 = 0⇒ 2k

^{2}= −36⇒ k

^{2}= −18⇒ k =

⇒ k =

⇒ k =

⇒ k = 3√2i

**Question 3. Find k if 2k ^{2} + 400 = 0.**

**Solution:**

2k

^{2}+ 400 = 0⇒ 2k

^{2}= −400⇒ k

^{2}= −200⇒ k =

⇒ k =

⇒ k =

⇒ k = 10√2i

**Question 4. Find k if 2k ^{2} + 100 = 0.**

**Solution:**

2k

^{2}+ 100 = 0⇒ 2k

^{2}= −100⇒ k

^{2}= −50⇒ k =

⇒ k =

⇒ k =

⇒ k = 5√2i

**Question 5. Find k if 2k ^{2} + 256 = 0.**

**Solution:**

2k2 + 256 = 0

⇒ 2k2 = −256

⇒ k

^{2}= −128⇒ k =

⇒ k =

⇒ k =

⇒ k = 8√2i