urgent help required in these two q (1 Viewer)

ExtremelyBoredUser · Dec 3, 2021

amdspotter said:
View attachment 34405

9.

let z = x + iy

first eqn:
$|z|^2 = 5$
$x^2+y^2 = 5$

second eqn:
multiply the fraction by z for both denominator and numerator
$\frac{z^2}{|z|^2} = \frac{1}{5} \times (3+4i)$
|z|^2 = 5 from first eqn so just cancel them out.

$z^2 = (3+4i)$
$x^2 - y^2 + 2xiy = (3+4i)$

Equate both real and imaginary parts and solve like any square root type of question

10.a

$z^2 - 2z\cos(x) + 1 = 0$
$z^2 - 2z\cos(x) + \cos^2(x) + 1 = \cos^2(x)$
$z^2 - 2z\cos(x) + \cos^2(x) + 1 = \cos^2(x)$
$(z - \cos(x) )^2 = \cos^2(x) - 1$
$(z - \cos(x) )^2 = -\sin^2(x)$
$z - \cos(x) = i\sin(x)$ or $z - \cos(x) = - i\sin(x)$
$z = \cos(x) + i\sin(x)$ or $z = \cos(x) - i\sin(x)$

b.

just substitution

5uckerberg · Dec 3, 2021

I remember that the first question was answered from a previous thread by =)(= somewhere or somebody. Just want one of the moderators to confirm.

Run hard@thehsc · Dec 3, 2021

@5uckerberg Yea true I saw this elsewhere as well!

urgent help required in these two q (1 Viewer)

amdspotter

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ExtremelyBoredUser

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5uckerberg

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Run hard@thehsc

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