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"# Questions 10 -13"
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"## Q10 Roots\n",
"Find the four roots of $(-3)^{1/4}$.\n",
"\n",
"**Strategy:** This problem is the same as solving the equation $w^4 = -3$ and as there are four roots they must form a square on an Argand diagram whose corners lie on a circle of radius $3^{1/4}$. The roots of a negative number are sought so these must all be complex with a zero real part; i.e. with an imaginary part only.\n",
"\n",
"## Q11 Square roots\n",
"Find the square roots of $i$, i.e. $w^2 = i$. Find their magnitude and plot them on an Argand diagram.\n",
"\n",
"## Q12 Solve eqn.\n",
"Solve $w^4 = 16$.\n",
"\n",
"**Strategy:** Because the equation is fourth order, there are four solutions and not just the two real ones $w = \\pm 2$. Use the method of previous questions.\n",
"\n",
"## Q13 Modulus & argument\n",
"Calculate the modulus and argument of $2 + 3i$ then calculate its square roots. What is the radius of the circle on which the roots lie and at what angles?\n",
"\n",
"**Strategy:** The complex number $2 + 3i$ is best converted into its trigonometric form to calculate the modulus and argument."
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