Question

6i5+7i4 +3i3 +5i2-4 in the form of a+ib anad find its square root

Answer 1

6i⁵ + 7i⁴ + 3i³ + 5i² - 4 = - 2 + 3i

Step-by-step explanation:

We know that,

• i = √(- 1)

• i² = - 1

Now, 6i⁵ + 7i⁴ + 3i³ + 5i² - 4

= 6 (i⁴ * i) + 7 (i⁴) + 3 (i² * i) + 5 (i²) - 4

= 6 {(i²)² * i} + 7 (i²)² + 3 (i² * i) + 5 (i²) - 4

= 6 {(- 1)² * i} + 7 (- 1)² + 3 {(- 1) * i} + 5 (- 1) - 4

= 6i + 7 - 3i - 5 - 4

= - 2 + 3i, which is in the form of a + ib

Note: To calculate this type of problems, first try to find if there is any exponent in terms of i. Reduce them to the smallest expression, in terms of i only.