# Complex Number Power Formula

The complex number power formula is used to compute the value of a complex number which is raised to the power of “n”. To recall, a complex number is the form of x + y,1, where x and y are the real numbers and “i” is an imaginary number. The “i” satisfies i2 = -1.

## Formula to Calculate the Power of a Complex Number

The complex number power formula is given below.

 zn = (reIθ )n = rn einθ

Example Question

Question 1:Compute: (3+3i)5

Solution:

Here is the exponential form of 3+3i

r = √ (9+9) = 3 √2

tan θ = (3/3)

⇒arg z = (π/4)

3 + 3i = 3√2ei(π/4)

Now, (3 + 3i)5 = (3 √2)5 ei(5π/4)

= 972 √2 (cos(5π/4) + isin (5π/4))

= 972 √2 [(−√2/2)−(√2/2)i]

= − 972 − 972i

#### Practise This Question

Dehalogenation of meso-2, 3-dibromo-butane results in