# Answer the following: Convert the complex numbers in polar form and also in exponential form. z = -6+2i - Mathematics and Statistics

Sum

Convert the complex numbers in polar form and also in exponential form.

z = -6 + sqrt(2)"i"

#### Solution

z = -6 + sqrt(2)"i"

∴ a = – 6, b = sqrt(2), i.e. a < 0, b > 0

∴ r = sqrt("a"^2 + "b"^2)

= sqrt((-6)^2 + (sqrt(2))^2

= sqrt(36 + 2)

= sqrt(38)

Here (-6, sqrt(2)) lies in 2nd quadrant

∴ amp (z) = θ

= pi + tan^-1("b"/"a")

= tan^-1(-sqrt(2)/6) + pi

∴ the polar form of z = r(cos θ + i sin θ)

∴ sqrt(38)(cos theta + "i" sin theta), where θ

= pi + tan^-1(-sqrt(2)/6)

∴ The exponential form of z = re

sqrt(38)"e" ^(pi + tan^-1(-sqrt(2)/6)

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#### APPEARS IN

Balbharati Mathematics and Statistics 2 (Arts and Science) 11th Standard Maharashtra State Board
Chapter 1 Complex Numbers
Miscellaneous Exercise 1 | Q II. (12) (ii) | Page 22