write 6i5 7i4 3i3 5i2 4 in the form of a+ib and find its square root
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Answer:
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.
Step-by-step explanation:
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