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## Homework Statement

show that [tex]\sqrt{1+ja}[/tex] is equivalent to [tex]\pm(1+j)(a/2)^{1/2}[/tex] with a>>1

## Homework Equations

Euler's formula?

## The Attempt at a Solution

with a>>1

|z| = [tex]\sqrt{(1 + a^{2})}[/tex] == a

lim a-->infinity arctan (a/1) == [tex]\pi/2[/tex]

[tex]\sqrt{z}[/tex] = [tex]\sqrt{(ae^{j\pi/2})}[/tex]

[tex]\sqrt{z}[/tex] = [tex]\pmsqrt a^{1/2} e^{j1.25}[/tex]

However, when I transfer back to complex form, I don't get it to equal 1+j. Not too sure how they got a/2 as well.

Any tips would be great.