Complex Basics
Evaluate i2.
What is -1?
Simplify (3+2i)+(5-7i).
What is 8-5i?
Find |3+4i|.
What is 5?
Write (1+i) in polar form.
What is √2[cos(pi/4)+isin(pi/4)]?
Describe the locus |z|=4.
What is a circle centred at the origin with radius 4.
Simplify i15.
What is -i?
Expand (2+3i)(4-i).
What is 11+10i?
Find the modulus of (-5+12i).
What is 13?
Convert What is 2[cos(pi/3)+isin(pi/3)] to Cartesian form.
What is 1+√3i?
Describe |z-(2+3i)|=5.
What is a circle centred at (2,3) with radius 5?
If z=-4+7i, state Re(z) and Im(z).
What is Re(z)=-4, Im(z)=7?
State the conjugate of (-5+8i).
What is -5-8i?
Find the principal argument of 1+i.
What is pi/4?
If z=2[cos(pi/6)+isin(pi/6)], find z3.
What is 8i.
Describe the locus |z-(1+2i)|=|z-(5+2i)|.
What is the perpendicular bisector of the line joining (1,2) and (5,2), i.e. x=3?
Find x and y if (2x-3)+(y+4)i=7-2i.
What is x=5, y=-6?
Express in the form (a+bi):
(3+4i)/(1-2i).
What is -1+2i?
Find the principal argument of -1-√3i.
What is -2pi/3?
Use De Moivre’s theorem to simplify [cos(Θ)+isin(Θ)]5.
What is cos(5Θ)+isin(5Θ)?
Describe the locus arg(z-2)=pi/4.
What is a ray starting at (2,0), making an angle of pi/4 with the positive real axis, with (2,0) excluded?
Find the square roots of 5+12i.
What is +-(3+2i)?
Solve: z2-6z+13=0
What is z=3(+-)2i
Given z=-5+12i, find |z| and the principal argument of z.
What is |z|=13, arg(z)=pi+tan-1(12/5)?
Use De Moivre’s theorem to express cos4Θ in terms of cosΘ.
What is cos4Θ=8cos4Θ-8cos2Θ+1?
Describe geometrically the locus of (z) satisfying |z-(2+i)|=2|z-(5+i)|.
This is a circle. (x-6)2+(y-1)2=4. Therefore, the locus is a circle with centre (6,1) and radius 2.