Question 10The complex number B is given by B (1- t) + (2t)i, where t is real.IItan)(i) Show that IB = 1 + t2 and arg(B) 0 where t = t(ii) Write down the modulus and argument of one square root of B, and hence if z2 = B, write z inthe form a + ib where a and b are real.(iii) Hence find the two square roots of -8+ 6i

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Asked Oct 27, 2019
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[Lin WS - Question 10]

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Question 10
The complex number B is given by B (1- t) + (2t)i, where t is real.
II
tan)
(i) Show that IB = 1 + t2 and arg(B) 0 where t = t
(ii) Write down the modulus and argument of one square root of B, and hence if z2 = B, write z in
the form a + ib where a and b are real.
(iii) Hence find the two square roots of -8+ 6i
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Question 10 The complex number B is given by B (1- t) + (2t)i, where t is real. II tan) (i) Show that IB = 1 + t2 and arg(B) 0 where t = t (ii) Write down the modulus and argument of one square root of B, and hence if z2 = B, write z in the form a + ib where a and b are real. (iii) Hence find the two square roots of -8+ 6i

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Expert Answer

Step 1

The problem concerns the algebraic operations in Complex numbers

Step 2

Definitions and notations : here x is the real part and y the imaginary part of the complex number z.

Ifxtythen
y
EVx,r(-)= tan
х
(x, ye R)
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Ifxtythen y EVx,r(-)= tan х (x, ye R)

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Step 3

Computing |B...

For z B,x 1-.y- 21, so
= Y(1-f + 4r = vi-2r +r +4r
= 1+2r2 +f°
=1+r
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For z B,x 1-.y- 21, so = Y(1-f + 4r = vi-2r +r +4r = 1+2r2 +f° =1+r

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