W15 Stepwise

Due date: Thursday 4/23, 11:59pm

01

01

Complex arithmetic

Write each of these expressions in the form $a+bi$.

(a) $(1+3i)(5-i)$ (b) $\frac{2+5i}{-3+7i}$

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02

02

Complex solutions of quadratic equations

Find all solutions and write them in the form $z=a+bi$.

$$2z^2+z+1=0$$

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03

01

Complex forms - exponential to Cartesian

Write each number in the form $a+bi$.

(a) $2e^{i\frac{\pi }{4}}$ (b) $e^{\ln 4+i\frac{\pi }{2}}$

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04

02

Polar and exponential form

Write down Euler’s Formula.

Now write $-5+5i$:

(i) in polar form (ii) in exponential form

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05

01

Complex roots using polar

Find the three cube ($3^{\text{rd}}$) roots of $27i$.

Write your answer in the form $a+bi$.

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